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pretraining/mathematica/algebra/log_equations/10768.txt

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+Problem:
+Find all real solutions to $\frac{\log \left(x+\frac{15}{2}\right)}{\log (8)}+\frac{\log (-24 x-18)}{\log (8)}=\frac{\log (12 x+13)}{\log (8)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{24} \left(-105-\sqrt{7473}\right)\right\},\left\{x\to \frac{1}{24} \left(-105+\sqrt{7473}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/11303.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+20)}{\log (5)}+\frac{\log (5 x-23)}{\log (5)}=\frac{\log (15 x-21)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{5} \left(-31-2 \sqrt{789}\right)\right\},\left\{x\to \frac{1}{5} \left(-31+2 \sqrt{789}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/11920.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-12)}{\log (7)}+\frac{\log (10-23 x)}{\log (7)}=\frac{\log (9-9 x)}{\log (7)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{46} \left(295-\sqrt{75157}\right)\right\},\left\{x\to \frac{1}{46} \left(295+\sqrt{75157}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/14122.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+21)}{\log (5)}+\frac{\log (-7 x-14)}{\log (5)}=\frac{\log (23-x)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{7} \left(-80-\sqrt{4181}\right)\right\},\left\{x\to \frac{1}{7} \left(-80+\sqrt{4181}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/14148.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+24)}{\log (6)}+\frac{\log (-13 x-2)}{\log (6)}=\frac{\log (15 x-16)}{\log (6)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{26} \left(-329-\sqrt{106577}\right)\right\},\left\{x\to \frac{1}{26} \left(-329+\sqrt{106577}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/14898.txt

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+Problem:
+Find all real solutions to $\frac{\log \left(x-\frac{34}{5}\right)}{\log (2)}+\frac{\log \left(\frac{48 x}{5}+11\right)}{\log (2)}=\frac{\log \left(\frac{91 x}{5}-\frac{88}{5}\right)}{\log (2)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{120} \left(453-\sqrt{291009}\right)\right\},\left\{x\to \frac{1}{120} \left(453+\sqrt{291009}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/1564.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+9)}{\log (4)}+\frac{\log \left(22-\frac{11 x}{4}\right)}{\log (4)}=\frac{\log \left(20 x+\frac{23}{2}\right)}{\log (4)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{22} \left(-91-\sqrt{41105}\right)\right\},\left\{x\to \frac{1}{22} \left(-91+\sqrt{41105}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/16260.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-17)}{\log (8)}+\frac{\log (-16 x-9)}{\log (8)}=\frac{\log (1-20 x)}{\log (8)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{32} \left(283-7 \sqrt{1833}\right)\right\},\left\{x\to \frac{1}{32} \left(283+7 \sqrt{1833}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/16417.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-22)}{\log (7)}+\frac{\log (24 x+23)}{\log (7)}=\frac{\log (3-19 x)}{\log (7)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{24} \left(243-\sqrt{71265}\right)\right\},\left\{x\to \frac{1}{24} \left(243+\sqrt{71265}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/1654.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-8)}{\log (3)}+\frac{\log (6-19 x)}{\log (3)}=\frac{\log (19 x)}{\log (3)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{38} \left(139-\sqrt{15673}\right)\right\},\left\{x\to \frac{1}{38} \left(139+\sqrt{15673}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/16961.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-18)}{\log (7)}+\frac{\log (1-8 x)}{\log (7)}=\frac{\log (-19 x-6)}{\log (7)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{4} \left(41-\sqrt{1657}\right)\right\},\left\{x\to \frac{1}{4} \left(41+\sqrt{1657}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/17917.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+4)}{\log (9)}+\frac{\log (15 x+1)}{\log (9)}=\frac{\log (22 x+3)}{\log (9)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{30} \left(-39-\sqrt{1461}\right)\right\},\left\{x\to \frac{1}{30} \left(-39+\sqrt{1461}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/18111.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+20)}{\log (5)}+\frac{\log (-9 x-20)}{\log (5)}=\frac{\log (10-7 x)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{18} \left(-193-\sqrt{22489}\right)\right\},\left\{x\to \frac{1}{18} \left(-193+\sqrt{22489}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/18567.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-24)}{\log (5)}+\frac{\log (15-10 x)}{\log (5)}=\frac{\log (-13 x-2)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{5} \left(67-\sqrt{3594}\right)\right\},\left\{x\to \frac{1}{5} \left(67+\sqrt{3594}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/20722.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+7)}{\log (4)}+\frac{\log (13 x-12)}{\log (4)}=\frac{\log (9 x+24)}{\log (4)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{13} \left(-35-\sqrt{2629}\right)\right\},\left\{x\to \frac{1}{13} \left(-35+\sqrt{2629}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/20861.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-12)}{\log (3)}+\frac{\log (-6 x-6)}{\log (3)}=\frac{\log (12 x-8)}{\log (3)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{6} \left(27-\sqrt{1209}\right)\right\},\left\{x\to \frac{1}{6} \left(27+\sqrt{1209}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/21044.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+11)}{\log (2)}+\frac{\log (21 x-10)}{\log (2)}=\frac{\log (23-14 x)}{\log (2)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{42} \left(-235-\sqrt{66397}\right)\right\},\left\{x\to \frac{1}{42} \left(-235+\sqrt{66397}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/21409.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-1)}{\log (5)}+\frac{\log (-3 x-17)}{\log (5)}=\frac{\log (10 x+25)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{3} \left(-12-2 \sqrt{30}\right)\right\},\left\{x\to \frac{1}{3} \left(-12+2 \sqrt{30}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/21463.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-3)}{\log (3)}+\frac{\log (15 x-10)}{\log (3)}=\frac{\log (13 x+17)}{\log (3)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{5}\right\},\left\{x\to \frac{13}{3}\right\}\right\}$

pretraining/mathematica/algebra/log_equations/22276.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-11)}{\log (5)}+\frac{\log (x+14)}{\log (5)}=\frac{\log (-10 x-8)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{2} \left(-13-\sqrt{753}\right)\right\},\left\{x\to \frac{1}{2} \left(-13+\sqrt{753}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/22662.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-15)}{\log (4)}+\frac{\log (-10 x-11)}{\log (4)}=\frac{\log (-3 x-13)}{\log (4)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{10} \left(71-\sqrt{6821}\right)\right\},\left\{x\to \frac{1}{10} \left(71+\sqrt{6821}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/23049.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+3)}{\log (5)}+\frac{\log (-22 x-21)}{\log (5)}=\frac{\log \left(\frac{25 x}{2}+5\right)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{88} \left(-199-\sqrt{15665}\right)\right\},\left\{x\to \frac{1}{88} \left(-199+\sqrt{15665}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/24081.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-6)}{\log (2)}+\frac{\log (12 x+2)}{\log (2)}=\frac{\log (14-2 x)}{\log (2)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{6} \left(17-\sqrt{367}\right)\right\},\left\{x\to \frac{1}{6} \left(17+\sqrt{367}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/24288.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+19)}{\log (8)}+\frac{\log (7-12 x)}{\log (8)}=\frac{\log (6 x+17)}{\log (8)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{24} \left(-227-\sqrt{57097}\right)\right\},\left\{x\to \frac{1}{24} \left(-227+\sqrt{57097}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/24448.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-24)}{\log (9)}+\frac{\log (14 x-9)}{\log (9)}=\frac{\log (9 x+14)}{\log (9)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{14} \left(177-\sqrt{28501}\right)\right\},\left\{x\to \frac{1}{14} \left(177+\sqrt{28501}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/25618.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+22)}{\log (9)}+\frac{\log (-17 x-21)}{\log (9)}=\frac{\log (3 x-7)}{\log (9)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{17} \left(-199-\sqrt{31866}\right)\right\},\left\{x\to \frac{1}{17} \left(-199+\sqrt{31866}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/25830.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+20)}{\log (5)}+\frac{\log (-15 x-14)}{\log (5)}=\frac{\log (6-25 x)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{30} \left(-289-\sqrt{66361}\right)\right\},\left\{x\to \frac{1}{30} \left(-289+\sqrt{66361}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/26512.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-17)}{\log (8)}+\frac{\log \left(\frac{95 x}{4}-\frac{19}{4}\right)}{\log (8)}=\frac{\log \left(-\frac{49 x}{2}-\frac{49}{2}\right)}{\log (8)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{95} \left(768-49 \sqrt{229}\right)\right\},\left\{x\to \frac{1}{95} \left(768+49 \sqrt{229}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/27836.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-16)}{\log (4)}+\frac{\log (-25 x-21)}{\log (4)}=\frac{\log (8 x-8)}{\log (4)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{50} \left(371-\sqrt{172041}\right)\right\},\left\{x\to \frac{1}{50} \left(371+\sqrt{172041}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/2844.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-16)}{\log (7)}+\frac{\log (-11 x-8)}{\log (7)}=\frac{\log (19 x+5)}{\log (7)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{22} \left(149-\sqrt{27613}\right)\right\},\left\{x\to \frac{1}{22} \left(149+\sqrt{27613}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/29888.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-12)}{\log (2)}+\frac{\log (12 x+12)}{\log (2)}=\frac{\log (12-7 x)}{\log (2)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{24} \left(125-\sqrt{23113}\right)\right\},\left\{x\to \frac{1}{24} \left(125+\sqrt{23113}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/30479.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-8)}{\log (4)}+\frac{\log (21 x-14)}{\log (4)}=\frac{\log (17 x-11)}{\log (4)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{42} \left(199-\sqrt{29269}\right)\right\},\left\{x\to \frac{1}{42} \left(199+\sqrt{29269}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/30529.txt

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+Problem:
+Find all real solutions to $\frac{\log \left(x+\frac{108}{7}\right)}{\log (5)}+\frac{\log \left(\frac{43}{7}-15 x\right)}{\log (5)}=\frac{\log \left(\frac{167 x}{7}-\frac{145}{7}\right)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{105} \left(-872-\sqrt{845269}\right)\right\},\left\{x\to \frac{1}{105} \left(-872+\sqrt{845269}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/31378.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+8)}{\log (6)}+\frac{\log (-14 x-17)}{\log (6)}=\frac{\log (21 x+8)}{\log (6)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{14} \left(-75-3 \sqrt{401}\right)\right\},\left\{x\to \frac{1}{14} \left(-75+3 \sqrt{401}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/32496.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-18)}{\log (2)}+\frac{\log (18 x+25)}{\log (2)}=\frac{\log (23 x-5)}{\log (2)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{18} \left(161-\sqrt{33931}\right)\right\},\left\{x\to \frac{1}{18} \left(161+\sqrt{33931}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/32696.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+21)}{\log (7)}+\frac{\log (-17 x-5)}{\log (7)}=\frac{\log (12-6 x)}{\log (7)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{17} \left(-178-\sqrt{29695}\right)\right\},\left\{x\to \frac{1}{17} \left(-178+\sqrt{29695}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/33876.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-20)}{\log (7)}+\frac{\log (22 x-7)}{\log (7)}=\frac{\log (-7 x)}{\log (7)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{11} \left(110-\sqrt{11330}\right)\right\},\left\{x\to \frac{1}{11} \left(110+\sqrt{11330}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/3389.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-15)}{\log (2)}+\frac{\log (3 x+22)}{\log (2)}=\frac{\log (8 x+20)}{\log (2)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{6} \left(31-\sqrt{5161}\right)\right\},\left\{x\to \frac{1}{6} \left(31+\sqrt{5161}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/34082.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-12)}{\log (2)}+\frac{\log (15-x)}{\log (2)}=\frac{\log (-6 x-9)}{\log (2)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{2} \left(33-9 \sqrt{5}\right)\right\},\left\{x\to \frac{1}{2} \left(33+9 \sqrt{5}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/34151.txt

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+Problem:
+Find all real solutions to $\frac{\log \left(x-\frac{14}{5}\right)}{\log (7)}+\frac{\log \left(-\frac{114 x}{5}-\frac{13}{5}\right)}{\log (7)}=\frac{\log \left(\frac{23}{5}-\frac{41 x}{5}\right)}{\log (7)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{570} \left(868-\sqrt{791614}\right)\right\},\left\{x\to \frac{1}{570} \left(868+\sqrt{791614}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/35.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+6)}{\log (6)}+\frac{\log (4-18 x)}{\log (6)}=\frac{\log (-11 x-3)}{\log (6)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{12} \left(-31-\sqrt{1177}\right)\right\},\left\{x\to \frac{1}{12} \left(-31+\sqrt{1177}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/35245.txt

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+Problem:
+Find all real solutions to $\frac{\log \left(x+\frac{13}{2}\right)}{\log (5)}+\frac{\log \left(\frac{27 x}{2}-7\right)}{\log (5)}=\frac{\log \left(13 x+\frac{15}{2}\right)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{108} \left(-271-\sqrt{119233}\right)\right\},\left\{x\to \frac{1}{108} \left(-271+\sqrt{119233}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/35831.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+6)}{\log (4)}+\frac{\log (10-4 x)}{\log (4)}=\frac{\log (-19 x-7)}{\log (4)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{8} \left(5-\sqrt{1097}\right)\right\},\left\{x\to \frac{1}{8} \left(5+\sqrt{1097}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/36857.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-24)}{\log (2)}+\frac{\log (4 x+23)}{\log (2)}=\frac{\log (13 x+8)}{\log (2)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{4} \left(43-\sqrt{4089}\right)\right\},\left\{x\to \frac{1}{4} \left(43+\sqrt{4089}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/37174.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+4)}{\log (5)}+\frac{\log (21-24 x)}{\log (5)}=\frac{\log (24 x+5)}{\log (5)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{48} \left(-99-\sqrt{17385}\right)\right\},\left\{x\to \frac{1}{48} \left(-99+\sqrt{17385}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/3761.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+23)}{\log (6)}+\frac{\log (20-18 x)}{\log (6)}=\frac{\log (-9 x-16)}{\log (6)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{36} \left(-385-29 \sqrt{217}\right)\right\},\left\{x\to \frac{1}{36} \left(-385+29 \sqrt{217}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/37826.txt

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+Problem:
+Find all real solutions to $\frac{\log (x+4)}{\log (3)}+\frac{\log (x+4)}{\log (3)}=\frac{\log (11-18 x)}{\log (3)}$
+Answer:
+$\left\{\left\{x\to -13-2 \sqrt{41}\right\},\left\{x\to -13+2 \sqrt{41}\right\}\right\}$

pretraining/mathematica/algebra/log_equations/37989.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-5)}{\log (4)}+\frac{\log (21 x+1)}{\log (4)}=\frac{\log (2 x+7)}{\log (4)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{21} \left(53-\sqrt{3061}\right)\right\},\left\{x\to \frac{1}{21} \left(53+\sqrt{3061}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/38738.txt

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+Problem:
+Find all real solutions to $\frac{\log (x-16)}{\log (2)}+\frac{\log (8 x-23)}{\log (2)}=\frac{\log (x)}{\log (2)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{2} \left(19-\sqrt{177}\right)\right\},\left\{x\to \frac{1}{2} \left(19+\sqrt{177}\right)\right\}\right\}$

pretraining/mathematica/algebra/log_equations/39066.txt

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+Problem:
+Find all real solutions to $\frac{\log \left(x+\frac{46}{3}\right)}{\log (9)}+\frac{\log \left(\frac{17 x}{3}+\frac{11}{3}\right)}{\log (9)}=\frac{\log \left(\frac{47}{3}-\frac{7 x}{3}\right)}{\log (9)}$
+Answer:
+$\left\{\left\{x\to \frac{1}{51} \left(-418-\sqrt{156109}\right)\right\},\left\{x\to \frac{1}{51} \left(-418+\sqrt{156109}\right)\right\}\right\}$