id
int64
1
14M
domain
stringclasses
6 values
topic
stringclasses
23 values
subtopic
stringclasses
37 values
difficulty
int64
1
8
unit_type
stringclasses
3 values
title
stringlengths
14
86
content
stringlengths
203
553
key_equations
stringclasses
23 values
prerequisites
stringclasses
29 values
learning_objective
stringclasses
37 values
1,501
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.406 x + 14.46 at x = -4.777
The linear relation y = m x + b with slope m = 1.406 and intercept b = 14.46 evaluated at x = -4.777 yields y = 7.743. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,502
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.111 x + 15.69 at x = -4.024
The linear relation y = m x + b with slope m = 2.111 and intercept b = 15.69 evaluated at x = -4.024 yields y = 7.2. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,503
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.501 x + 10.62 at x = 7.994
The linear relation y = m x + b with slope m = -3.501 and intercept b = 10.62 evaluated at x = 7.994 yields y = -17.36. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,504
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.054 x + 12.09 at x = 2.001
The linear relation y = m x + b with slope m = 3.054 and intercept b = 12.09 evaluated at x = 2.001 yields y = 18.21. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,505
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.605 x + 7.23 at x = 4.426
The linear relation y = m x + b with slope m = 1.605 and intercept b = 7.23 evaluated at x = 4.426 yields y = 14.33. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,506
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.554 x + 19.9 at x = -4.811
The linear relation y = m x + b with slope m = 1.554 and intercept b = 19.9 evaluated at x = -4.811 yields y = 12.42. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,507
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.8143 x + -4.469 at x = -9.294
The linear relation y = m x + b with slope m = -0.8143 and intercept b = -4.469 evaluated at x = -9.294 yields y = 3.099. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,508
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.081 x + 2.882 at x = -6.202
The linear relation y = m x + b with slope m = 2.081 and intercept b = 2.882 evaluated at x = -6.202 yields y = -10.02. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,509
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.265 x + -11.11 at x = 0.6927
The linear relation y = m x + b with slope m = 2.265 and intercept b = -11.11 evaluated at x = 0.6927 yields y = -9.536. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,510
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.849 x + 16.26 at x = 3.437
The linear relation y = m x + b with slope m = 2.849 and intercept b = 16.26 evaluated at x = 3.437 yields y = 26.05. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,511
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.07315 x + 13.82 at x = 6.813
The linear relation y = m x + b with slope m = 0.07315 and intercept b = 13.82 evaluated at x = 6.813 yields y = 14.32. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,512
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.765 x + -12.75 at x = -8.048
The linear relation y = m x + b with slope m = 3.765 and intercept b = -12.75 evaluated at x = -8.048 yields y = -43.05. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,513
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.721 x + -9.654 at x = 6.167
The linear relation y = m x + b with slope m = -3.721 and intercept b = -9.654 evaluated at x = 6.167 yields y = -32.6. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,514
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.629 x + -12.68 at x = 3.594
The linear relation y = m x + b with slope m = 2.629 and intercept b = -12.68 evaluated at x = 3.594 yields y = -3.227. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,515
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.644 x + -16.43 at x = -2.894
The linear relation y = m x + b with slope m = -1.644 and intercept b = -16.43 evaluated at x = -2.894 yields y = -11.67. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,516
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.442 x + -7.717 at x = 5.762
The linear relation y = m x + b with slope m = 2.442 and intercept b = -7.717 evaluated at x = 5.762 yields y = 6.354. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,517
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.687 x + -9.578 at x = -4.119
The linear relation y = m x + b with slope m = -1.687 and intercept b = -9.578 evaluated at x = -4.119 yields y = -2.63. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,518
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.512 x + -1.179 at x = 7.328
The linear relation y = m x + b with slope m = 3.512 and intercept b = -1.179 evaluated at x = 7.328 yields y = 24.56. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,519
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.8357 x + 17.77 at x = -8.576
The linear relation y = m x + b with slope m = 0.8357 and intercept b = 17.77 evaluated at x = -8.576 yields y = 10.6. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,520
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.894 x + 0.01909 at x = 7.35
The linear relation y = m x + b with slope m = 3.894 and intercept b = 0.01909 evaluated at x = 7.35 yields y = 28.64. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,521
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.183 x + -8.066 at x = -8.919
The linear relation y = m x + b with slope m = -1.183 and intercept b = -8.066 evaluated at x = -8.919 yields y = 2.488. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,522
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.542 x + -14.51 at x = -5.994
The linear relation y = m x + b with slope m = 3.542 and intercept b = -14.51 evaluated at x = -5.994 yields y = -35.74. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,523
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.9081 x + 2.776 at x = 8.132
The linear relation y = m x + b with slope m = -0.9081 and intercept b = 2.776 evaluated at x = 8.132 yields y = -4.609. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,524
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.4243 x + -7.345 at x = 4.313
The linear relation y = m x + b with slope m = -0.4243 and intercept b = -7.345 evaluated at x = 4.313 yields y = -9.175. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,525
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.789 x + -0.4968 at x = 2.621
The linear relation y = m x + b with slope m = 2.789 and intercept b = -0.4968 evaluated at x = 2.621 yields y = 6.813. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,526
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.232 x + 5.38 at x = -9.906
The linear relation y = m x + b with slope m = -3.232 and intercept b = 5.38 evaluated at x = -9.906 yields y = 37.39. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,527
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -2.265 x + 10.45 at x = -6.628
The linear relation y = m x + b with slope m = -2.265 and intercept b = 10.45 evaluated at x = -6.628 yields y = 25.46. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,528
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.645 x + -0.4169 at x = 5.271
The linear relation y = m x + b with slope m = 2.645 and intercept b = -0.4169 evaluated at x = 5.271 yields y = 13.53. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,529
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.12 x + 4.579 at x = 2.67
The linear relation y = m x + b with slope m = -4.12 and intercept b = 4.579 evaluated at x = 2.67 yields y = -6.419. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,530
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.9661 x + 18.61 at x = -2.334
The linear relation y = m x + b with slope m = -0.9661 and intercept b = 18.61 evaluated at x = -2.334 yields y = 20.87. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,531
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.623 x + -12.02 at x = -2.538
The linear relation y = m x + b with slope m = -4.623 and intercept b = -12.02 evaluated at x = -2.538 yields y = -0.291. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,532
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.859 x + -7.111 at x = 6.665
The linear relation y = m x + b with slope m = -4.859 and intercept b = -7.111 evaluated at x = 6.665 yields y = -39.5. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,533
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.094 x + 7.07 at x = 2.534
The linear relation y = m x + b with slope m = -3.094 and intercept b = 7.07 evaluated at x = 2.534 yields y = -0.7701. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,534
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -2.512 x + 7.741 at x = -3.113
The linear relation y = m x + b with slope m = -2.512 and intercept b = 7.741 evaluated at x = -3.113 yields y = 15.56. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,535
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.711 x + -4.658 at x = 1.773
The linear relation y = m x + b with slope m = -3.711 and intercept b = -4.658 evaluated at x = 1.773 yields y = -11.24. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,536
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.33 x + 12.95 at x = -4.036
The linear relation y = m x + b with slope m = -3.33 and intercept b = 12.95 evaluated at x = -4.036 yields y = 26.39. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,537
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -2.092 x + 9.113 at x = 1.927
The linear relation y = m x + b with slope m = -2.092 and intercept b = 9.113 evaluated at x = 1.927 yields y = 5.082. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,538
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.622 x + 15.52 at x = 9.909
The linear relation y = m x + b with slope m = -1.622 and intercept b = 15.52 evaluated at x = 9.909 yields y = -0.5507. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,539
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.573 x + 16.06 at x = -2.815
The linear relation y = m x + b with slope m = -1.573 and intercept b = 16.06 evaluated at x = -2.815 yields y = 20.48. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,540
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.116 x + 17.92 at x = 8.364
The linear relation y = m x + b with slope m = -3.116 and intercept b = 17.92 evaluated at x = 8.364 yields y = -8.137. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,541
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.9661 x + -10.86 at x = 4.543
The linear relation y = m x + b with slope m = -0.9661 and intercept b = -10.86 evaluated at x = 4.543 yields y = -15.25. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,542
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.688 x + 9.363 at x = 1.794
The linear relation y = m x + b with slope m = -3.688 and intercept b = 9.363 evaluated at x = 1.794 yields y = 2.747. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,543
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.31 x + -5.336 at x = 3.011
The linear relation y = m x + b with slope m = -3.31 and intercept b = -5.336 evaluated at x = 3.011 yields y = -15.3. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,544
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.626 x + 15.06 at x = -4.884
The linear relation y = m x + b with slope m = -4.626 and intercept b = 15.06 evaluated at x = -4.884 yields y = 37.66. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,545
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.3473 x + -18.06 at x = 9.894
The linear relation y = m x + b with slope m = 0.3473 and intercept b = -18.06 evaluated at x = 9.894 yields y = -14.62. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,546
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.62 x + 6.143 at x = -9.605
The linear relation y = m x + b with slope m = 1.62 and intercept b = 6.143 evaluated at x = -9.605 yields y = -9.415. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,547
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.897 x + -3.329 at x = -2.395
The linear relation y = m x + b with slope m = 1.897 and intercept b = -3.329 evaluated at x = -2.395 yields y = -7.873. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
1,548
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 3.693
The common logarithm log₁₀(3.693) = 0.5674. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,549
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.4929
The common logarithm log₁₀(0.4929) = -0.3072. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,550
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 6.8790e-05
The common logarithm log₁₀(6.8790e-05) = -4.162. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,551
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 219.9
The common logarithm log₁₀(219.9) = 2.342. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,552
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 36.62
The common logarithm log₁₀(36.62) = 1.564. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,553
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.004106
The common logarithm log₁₀(0.004106) = -2.387. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,554
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 87.09
The common logarithm log₁₀(87.09) = 1.94. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,555
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 89.08
The common logarithm log₁₀(89.08) = 1.95. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,556
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.001737
The common logarithm log₁₀(0.001737) = -2.76. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,557
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 18.52
The common logarithm log₁₀(18.52) = 1.268. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,558
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 4.4255e-05
The common logarithm log₁₀(4.4255e-05) = -4.354. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,559
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 9286
The common logarithm log₁₀(9286) = 3.968. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,560
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.8154e-05
The common logarithm log₁₀(1.8154e-05) = -4.741. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,561
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 421.9
The common logarithm log₁₀(421.9) = 2.625. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,562
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 2.5871e-05
The common logarithm log₁₀(2.5871e-05) = -4.587. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,563
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 2.3343e-05
The common logarithm log₁₀(2.3343e-05) = -4.632. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,564
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.8844e-05
The common logarithm log₁₀(1.8844e-05) = -4.725. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,565
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 2.4197e-04
The common logarithm log₁₀(2.4197e-04) = -3.616. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,566
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 2.4946e-04
The common logarithm log₁₀(2.4946e-04) = -3.603. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,567
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.001432
The common logarithm log₁₀(0.001432) = -2.844. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,568
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.896
The common logarithm log₁₀(1.896) = 0.2778. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,569
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 2.6307e-04
The common logarithm log₁₀(2.6307e-04) = -3.58. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,570
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 276.2
The common logarithm log₁₀(276.2) = 2.441. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,571
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.003501
The common logarithm log₁₀(0.003501) = -2.456. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,572
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 2.9708e-06
The common logarithm log₁₀(2.9708e-06) = -5.527. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,573
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.9042
The common logarithm log₁₀(0.9042) = -0.04374. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,574
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 3.1069e-04
The common logarithm log₁₀(3.1069e-04) = -3.508. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,575
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.5758e+05
The common logarithm log₁₀(1.5758e+05) = 5.197. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,576
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.009273
The common logarithm log₁₀(0.009273) = -2.033. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,577
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.0786e-06
The common logarithm log₁₀(1.0786e-06) = -5.967. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,578
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 114.7
The common logarithm log₁₀(114.7) = 2.06. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,579
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 7.6306e+04
The common logarithm log₁₀(7.6306e+04) = 4.883. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,580
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.0539e+04
The common logarithm log₁₀(1.0539e+04) = 4.023. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,581
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 106.7
The common logarithm log₁₀(106.7) = 2.028. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,582
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 6.1622e-05
The common logarithm log₁₀(6.1622e-05) = -4.21. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,583
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.2050e-05
The common logarithm log₁₀(1.2050e-05) = -4.919. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,584
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.382
The common logarithm log₁₀(1.382) = 0.1405. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,585
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 481.7
The common logarithm log₁₀(481.7) = 2.683. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,586
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.6424e-05
The common logarithm log₁₀(1.6424e-05) = -4.785. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,587
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.001177
The common logarithm log₁₀(0.001177) = -2.929. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,588
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 5.9419e-04
The common logarithm log₁₀(5.9419e-04) = -3.226. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,589
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 7.3112e+05
The common logarithm log₁₀(7.3112e+05) = 5.864. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,590
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.003567
The common logarithm log₁₀(0.003567) = -2.448. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,591
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.3727
The common logarithm log₁₀(0.3727) = -0.4287. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,592
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.5765e-05
The common logarithm log₁₀(1.5765e-05) = -4.802. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,593
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.2486e-04
The common logarithm log₁₀(1.2486e-04) = -3.904. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,594
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 2.9740e-06
The common logarithm log₁₀(2.9740e-06) = -5.527. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,595
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.003068
The common logarithm log₁₀(0.003068) = -2.513. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,596
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 4161
The common logarithm log₁₀(4161) = 3.619. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,597
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.005656
The common logarithm log₁₀(0.005656) = -2.248. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,598
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 728.6
The common logarithm log₁₀(728.6) = 2.862. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,599
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.3803e-05
The common logarithm log₁₀(1.3803e-05) = -4.86. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
1,600
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1254
The common logarithm log₁₀(1254) = 3.098. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.