## Precalculus: Mathematics for Calculus, 7th Edition

$\frac{3}{2}$
$Evaluate$ $the$ $expression$ $without$ $using$ $a$ $calculator:$ $\log_4 8$ 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: $\log_a a^x = x$ $$1 + \frac{1}{2} = \frac{3}{2}$$