SOLUTION: Solve: 5^ (2x-3) = 6^(3x)

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Question 91759: Solve: 5^ (2x-3) = 6^(3x)
Answer by mathispowerful(115) About Me  (Show Source):
You can put this solution on YOUR website!
In this equation we need to take logarithm on both sides:
log(5^2x-3) = log(6^3x)
then simplify it: (2x-3)log(5) = 3xlog(6)
expand the left side: 2xlog(5) - 3log(5) = 3xlog(6)
move x terms together: 2xlog(5) - 3xlog(6) = 3log(5)
combine x terms: x(2log(5) - 3log(6)) = 3log(5)
then: x+=+%283%2Alog%285%29%29%2F%282%2Alog%285%29-3%2Alog%286%29%29
or x+=+%28log%28125%29%29%2F%28log%2825%29+-+log%28216%29%29
If you need an numerical answer, it is x = -2.239
Hope this helps :)