Answer
$\frac{3}{2}$
Work Step by Step
$Evaluate$ $the$ $expression$ $without$ $using$ $a$ $calculator:$
$\log_4 8$
Use the First Law of Logarithms: $\log (AB) = \log A + \log B$
$$\log_4 (4\times2) = \log_4 4 + \log_4 2$$
$$1 + \log_4 2$$
Rewrite 2 as $4^{\frac{1}{2}}$ [ $4^{\frac{1}{2}} = \sqrt 4 = 2$]
$$1 +\log_4 4^{\frac{1}{2}}$$
Use the Third Property of Logarithms: $\log_a a^x = x$
$$1 + \frac{1}{2} = \frac{3}{2}$$
