# finding the value of x from a complex form of absolute value

How do I find the value of x for this one,

$$|x-3|^{\frac{x+1}{4}} = |x-3|^{\frac{x-2}{3}}$$

I tried equating the exponents when I found out that the base of both sides are equal but I don't think I'm doing it right. Please help.

HINT:

If $a^m=a^n$

either $(1)a=0$

or $(2)a^{m-n}=1\implies$

either $(i) a=1$

or $(ii)a=-1,m-n$ is even

or $(iii)m=n$