SOLUTION: I have to solve the equation {{{6^(5x-5)=8^(7x-6)}}} I took the natural logarithm of both sides so that I could use logarithm rules to get: {{{(5x-5)ln6=(7x-6)ln8}}} but I seem to

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I have to solve the equation {{{6^(5x-5)=8^(7x-6)}}} I took the natural logarithm of both sides so that I could use logarithm rules to get: {{{(5x-5)ln6=(7x-6)ln8}}} but I seem to      Log On


   

Question 973046: I have to solve the equation 6%5E%285x-5%29=8%5E%287x-6%29
I took the natural logarithm of both sides so that I could use logarithm rules to get: %285x-5%29ln6=%287x-6%29ln8 but I seem to be stuck at this step. I am not sure what to do next.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I have to solve the equation 6%5E%285x-5%29=8%5E%287x-6%29
I took the natural logarithm of both sides so that I could use logarithm rules to get: %285x-5%29ln6=%287x-6%29ln8 but I seem to be stuck at this step. I am not sure what to do next.
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%285x-5%29ln6=%287x-6%29ln8
Collect the terms with x.
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5x*ln(6) - 5ln(6) = 7x*ln(8) - 6ln(8)
5x*ln(6) - 7x*ln(8) = 5ln(6) - 6ln(8)
x*(5ln(6) - 7ln(8) = 5ln(6) - 6ln(8)
x = (5ln(6) - 6ln(8))/(5ln(6) - 7ln(8))
Calculator work now.