## Precalculus: Mathematics for Calculus, 7th Edition

$\frac{5}{2}$
$Evaluate$ $the$ $expression$ $without$ $using$ $a$ $calculator:$ $\log_3 \sqrt {243}$ Rewrite the root to exponent form $$\log_3 (243)^{\frac{1}{2}}$$ Rewrite 243 as $3^5$ [Note: $3^5 = 3\times3\times3\times3\times3 = 243$] $$\log_3 (3^5)^{\frac{1}{2}} \rightarrow \log_3 3^{\frac{5}{1}\times\frac{1}{2}}$$ $$\log_3 3^{\frac{5}{2}}$$ Use the Third Property of Logarithms: $\log_a a^x = x$ $$\log_3 3^{\frac{5}{2}} = \frac{5}{2}$$