Answer
$x=\frac{4}{3}$
Work Step by Step
RECALL:
(i) If $a^M=a^N$, then $M=N.$
(ii) $(a^m)^n=a^{mn}.$
Write 125 and 625 as powers of 5:
$125^{x}=625
\\(5^3)^x=5^4.$
Use rule (ii) above to obtain
$5^{3x}=5^4.$
Use rule (i) above to obtain
$3x=4
\\x=\frac{4}{3}.$
