Log(base)4(3x-7)=log(base)4(x-15) could somebody me out with this question? i don't even know where to begin.

The bases of the logarithms on either side of the equation are the same, which means that their arguments must be the same:

Put another way, we can write both sides as powers of 4, then simplify and eliminate the logarithms:

Then solve for :

Then we just have to check if this solution is valid. On the left side, we have

but we can't take logarithms of negative numbers, so there is no solution, as long as we're using the real-valued logarithm, anyway; is a solution if we use the complex-valued version.