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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.

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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 $(iii)m=n$

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