How to prove this theorem for exponential equations

Question

Prove that if $a^x=a^y a∈R$ then $x=y$ as in the exponential equation $2^x=2^3$

How can I prove this theorem, if you know what I mean

Answer 1

$a^x = a^y$
x.log a = y.log a

log a = 0 iff a = 1.
Draw your own conclusions.