Answer
(a) $x=2$
(b) $x=4$
Work Step by Step
(a)
We are given:
$\log_{x}16=4$
This means:
$x^{4}=16$
$x=\pm \sqrt[4]{16}=\pm 2$
$x=2$
(a log base can't be negative)
(b)
$\log_{x}8=\frac{3}{2}$
This means:
$ x^{3/2}=8$
$ x=8^{2/3}=4$