Answer
$x=\frac{3}{5}$
Work Step by Step
RECALL:
(i) If $a^M=a^N$, then $M=N.$
(ii) $(a^m)^n=a^{mn}$
Write 32 and 8 as powers of 2:
$32^{x}=8
\\(2^5)^x=2^3.$
Use rule (ii) above to obtain
$2^{5x}=2^3.$
Use rule (i) above to obtain
$5x=3
\\x=\frac{3}{5}.$
