Answer
$m = 18$
Work Step by Step
$\log_4(m-2) = 2$
$4^{2} = m-2$
$16 = m-2$
$16 + 2 = m$
$m = 18$
Check:
$\log_4(18-2) \overset{?}{=} 2$
$\log_4(16) \overset{?}{=} 2$
$\log_4(4^{2}) \overset{?}{=} 2$
$2\log_4(4) \overset{?}{=} 2$
$2(1)\overset{?}{=} 2$
$2 = 2$
