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1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:27:11
0a = 0
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
952,268,248,248,897,700
Noneuclidian
04/15/2022 23:29:15
But in the example I posted, there are two solutions, x = -6 and x = 0 . In the branch that determines x=-6, it looks like they just drop that first x? Or is "or" part of the statement itself?
1
0
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
952,268,248,248,897,700
Noneuclidian
04/15/2022 23:29:58
If you say x=0, then you shouldn't be able to do further evaluation of the x+6 inside the x(x+6)?
1
0
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
220,517,274,845,577,200
ramonov
04/15/2022 23:30:01
x=0 or x=-6
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
220,517,274,845,577,200
ramonov
04/15/2022 23:30:26
if x is 0, x(x+6) will be 0
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
220,517,274,845,577,200
ramonov
04/15/2022 23:30:35
if x=-6 x(x+6) will also be 0
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:31:00
f(x) = x(x+6) f(0) = 0(6) = 0 f(-6) = -6(0) = 0
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:32:26
Only one of the factors is 0 at a time. When we use the zero product property we are implicitly making the assumption that one of the factors is not zero and then solving for x
0
1
null
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null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:33:05
Because obviously we can't divide by 0
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
952,268,248,248,897,700
Noneuclidian
04/15/2022 23:35:45
Hmm I'm not sure if I'm fully satisfied with these answers. Thanks though. I'll work more of these examples
1
0
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:35:58
Ok look at it this way.
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:36:19
We have that: x(x+6) = 0
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:36:29
Now assume that (x+6) is not 0
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:36:39
So divide both sides by (x+6)
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:36:45
Then we get that x=0
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
952,268,248,248,897,700
Noneuclidian
04/15/2022 23:37:08
Okay, that I understand
1
0
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:37:16
And same thing for the other solution
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:37:48
x(x+6) = 0 Assume that x is not 0 So divide both sides by x x+6 = 0 x = -6
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
952,268,248,248,897,700
Noneuclidian
04/15/2022 23:38:57
Okay, that understand
1
0
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
952,268,248,248,897,700
Noneuclidian
04/15/2022 23:39:08
Thanks!
1
0
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
220,517,274,845,577,200
ramonov
04/15/2022 23:39:21
0 * stuff = 0 0 * x = 0 0 * (x+6) = 0
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:40:28
From a logical standpoint it does rely on casework and making these assumptions
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
952,268,248,248,897,700
Noneuclidian
04/15/2022 23:41:43
When I gave this problem to symolab it just whipped out the quadratic formula
1
0
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
551,269,104,800,104,450
EndTimes
04/15/2022 23:42:13
Try WolframAlpha instead, it's a bit smarter
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
952,268,248,248,897,700
Noneuclidian
04/15/2022 23:46:25
What other webapps do you guys recommend besides Symbolab and WolframAlpha for checking answers?
1
0
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
220,517,274,845,577,200
ramonov
04/15/2022 23:47:47
none
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
220,517,274,845,577,200
ramonov
04/15/2022 23:48:15
well i suppose desmos and geogebra for graphs
0
1
null
null
null
null
null
1,911
help-10
b13d7e50b4a644e9929fea2ce1d6d505
952,268,248,248,897,700
Noneuclidian
04/15/2022 23:58:36
Thanks
1
0
null
null
null
null
null
1,912
help-10
f731114cad4a4fe4a0601742a83ad6d4
703,317,182,683,021,400
duckecheese
04/16/2022 01:28:45
https://cdn.discordapp.c…7496/unknown.png
unknown.png
1
0
null
null
null
null
null
1,912
help-10
f731114cad4a4fe4a0601742a83ad6d4
703,317,182,683,021,400
duckecheese
04/16/2022 01:29:06
can someone tell me the first step in solving this
1
0
null
null
null
null
null
1,912
help-10
f731114cad4a4fe4a0601742a83ad6d4
118,536,946,527,109,120
Migillope
04/16/2022 01:29:22
close your other channel
0
1
null
null
null
null
null
1,912
help-10
f731114cad4a4fe4a0601742a83ad6d4
118,536,946,527,109,120
Migillope
04/16/2022 01:29:34
#help-7
0
1
null
null
null
null
null
1,912
help-10
f731114cad4a4fe4a0601742a83ad6d4
703,317,182,683,021,400
duckecheese
04/16/2022 01:29:44
how do i close
1
0
null
null
null
null
null
1,912
help-10
f731114cad4a4fe4a0601742a83ad6d4
703,317,182,683,021,400
duckecheese
04/16/2022 01:37:23
i fgiured it out
1
0
null
null
null
null
null
1,912
help-10
f731114cad4a4fe4a0601742a83ad6d4
703,317,182,683,021,400
duckecheese
04/16/2022 01:37:24
.close
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:15:41
Hello I am stuck on this question, I do not know how to proceed.
https://cdn.discordapp.c…reenshot_697.png
Screenshot_697.png
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:15:49
This is all I could do.
https://cdn.discordapp.c…936/IMG_2665.JPG
IMG_2665.JPG
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:16:01
Oh no it's tilted.
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:17:23
There we go.
https://cdn.discordapp.c…552/IMG_2665.jpg
IMG_2665.jpg
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
510,789,298,321,096,700
TeXit
11/13/2021 01:23:25
**kiid**
https://cdn.discordapp.c…971970191360.png
292286971970191360.png
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:23:36
none of solutions to choose from are in good form
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:23:43
ln(e) = 1 but they didn't factor that
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:23:55
Wait what.
1
0
551,269,104,800,104,450
EndTimes
8053
EndTimes
false
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:23:56
Oh.
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
292,286,971,970,191,360
kiid
11/13/2021 01:24:03
? one of them is correct
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:24:20
oh yeah i see im blind
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:24:20
lne just becomes 1 right?
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:24:38
Because log(e)e = 1.
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
292,286,971,970,191,360
kiid
11/13/2021 01:25:08
use $\log_a b^c = c \log_a b$ and $a^{\log_a k}=k$ to simplify $e^{x\ln a}$
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
510,789,298,321,096,700
TeXit
11/13/2021 01:25:11
**kiid**
https://cdn.discordapp.c…971970191360.png
292286971970191360.png
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:25:38
https://cdn.discordapp.c…11113_002520.jpg
20211113_002520.jpg
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
292,286,971,970,191,360
kiid
11/13/2021 01:26:14
why did you do it for them 😦
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:26:23
e^ln(ax) = a^x?
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:26:24
to explain it in concrete numbers
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:26:35
no
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:27:19
$$e^{a \cdot ln{x}} = e^{ln{(x^a)}}$$
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
510,789,298,321,096,700
TeXit
11/13/2021 01:27:36
**MattDog\_222**
https://cdn.discordapp.c…587749494784.png
205143587749494784.png
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:27:49
If there is a log anywhere in the equation I can bring the exponent to the front?
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:30:39
it goes both ways with this formula, idk what you mean by "anywhere"
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:30:45
the entire quantity is to said power
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:31:11
Oh uhh.
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:31:32
$$e^{3 \cdot ln{(3x^2+7x)}} = e^{ln{((3x^2+7x)^3)}} = (3x^2+7x)^3$$
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:31:58
Those are equivalent?
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:32:00
yes
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:32:09
I thought the 3 wouldn't affect the numbers inside like the cube does.
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
510,789,298,321,096,700
TeXit
11/13/2021 01:32:45
**MattDog\_222**
https://cdn.discordapp.c…587749494784.png
205143587749494784.png
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:32:49
all 3 of those are equal
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:33:07
Wait so the e or the ln is irrelevant here?
1
0
205,143,587,749,494,800
MattDog_222
1131
MattDog_222
false
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
567,490,557,572,546,600
boneslayer_suvy
11/13/2021 01:33:20
Basically
0
1
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null
null
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1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:33:26
Because the second and third one are basically the same except the third doesn't have ln or e.
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:33:40
because they cancel each other out since they share the natural base
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
769,113,579,403,608,000
カナン
11/13/2021 01:34:10
OH because ln = loge, and it's basically the same as log base e (e)?
1
0
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:38:22
$$ ln \neq log(e) $$
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
510,789,298,321,096,700
TeXit
11/13/2021 01:38:24
**MattDog\_222**
https://cdn.discordapp.c…587749494784.png
205143587749494784.png
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
205,143,587,749,494,800
MattDog_222
11/13/2021 01:38:43
$$ln(x) = log_e(x)$$
0
1
null
null
null
null
null
1,913
help-10
0196cb93ba3241ae932338f6b936ef66
510,789,298,321,096,700
TeXit
11/13/2021 01:38:46
**MattDog\_222**
https://cdn.discordapp.c…587749494784.png
205143587749494784.png
0
1
null
null
null
null
null
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help-10
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カナン
11/13/2021 01:40:01
This is 1 right?
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カナン
11/13/2021 01:40:16
Wait nvm.
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カナン
11/13/2021 01:40:45
Due to this the majority of the first bit is taken away, leaving us with a^x?
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MattDog_222
11/13/2021 01:41:13
wdym
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カナン
11/13/2021 01:41:31
In here.
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MattDog_222
11/13/2021 01:41:51
$$e^{x \cdot ln(a)} = e^{ln(a^x)}$$
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カナン
11/13/2021 01:41:54
You went from e^xlna to e^ln(a^x) so I assumed that you brought ln to the front.
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TeXit
11/13/2021 01:42:05
**MattDog\_222**
https://cdn.discordapp.c…587749494784.png
205143587749494784.png
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MattDog_222
11/13/2021 01:42:28
this is a logarithm law
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カナン
11/13/2021 01:42:36
Oh.
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MattDog_222
11/13/2021 01:42:41
well
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カナン
11/13/2021 01:42:42
So it can never be x^a?
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MattDog_222
11/13/2021 01:42:51
$$x \cdot ln(a) = ln(a^x)$$
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TeXit
11/13/2021 01:42:53
**MattDog\_222**
https://cdn.discordapp.c…587749494784.png
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MattDog_222
11/13/2021 01:42:56
is the law
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MattDog_222
11/13/2021 01:43:00
it just occures inside the exponent
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カナン
11/13/2021 01:43:15
Oh.
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MattDog_222
11/13/2021 01:43:30
and we need to do that so we can cancel the e and the ln
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カナン
11/13/2021 01:43:32
So we take the last number and raise it to the power of first number?
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MattDog_222
11/13/2021 01:43:44
huh?
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カナン
11/13/2021 01:43:56
Like we take a, and raise it to x.
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MattDog_222
11/13/2021 01:44:18
yes because its being multiplied on the outside, so its the same as raising to the power on the inside
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MattDog_222
11/13/2021 01:44:41
$$z \cdot ln(x+y) = ln((x+y)^z)$$
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TeXit
11/13/2021 01:44:44
**MattDog\_222**
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