Answer
$x=\frac{5}{2}$
Work Step by Step
RECALL:
(i) If $a^M=a^N$, then $M=N.$
(ii) $(a^m)^n=a^{mn}.$
Write 4 and 32 as powers of 2:
$4^{x}=32
\\(2^2)^x=2^5.$
Use rule (ii) above to obtain
$2^{2x}=2^5.$
Use rule (i) above to obtain
$2x=5
\\x=\frac{5}{2}.$
