Answer
$x=\frac{3}{2}$
Work Step by Step
RECALL:
(i) If $a^M=a^N$, then $M=N.$
(ii) $(a^m)^n=a^{mn}.$
Write 9 and 27 as powers of 3:
$9^{x}=27
\\(3^2)^x=3^3.$
Use rule (ii) above to obtain
$3^{2x}=3^3.$
Use rule (i) above to obtain
$2x=3
\\x=\frac{3}{2}.$
