Question 91759
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 = (3*log(5))/(2*log(5)-3*log(6))}}}

or {{{x = (log(125))/(log(25) - log(216))}}}

If you need an numerical answer, it is x = -2.239

Hope this helps :)