## Precalculus: Mathematics for Calculus, 7th Edition

$\log_2 (\frac{\sqrt{5}}{49})$
$Combine$ $the$ $expression$: $\frac{1}{2}$$\log_2 5 - 2$$\log_2 7$ Apply the Third Law of Logarithms for $\frac{1}{2}$$\log_2 5 and 2$$\log_2 7$ $\frac{1}{2}$$\log_2 5 = \log_2 5^\frac{1}{2} 2$$\log_2 7$ = $\log_2 7^2$ $\log_2 5^\frac{1}{2}$ - $\log_2 7^2$ $\log_2 \sqrt{5}$ - $\log_2 7^2$ [Note: 5$^\frac{1}{2}$ = $\sqrt{5}$] Apply the Second Law of Logarithms $\log_2 \sqrt{5}$ - $\log_2 7^2$ = $\log_2 (\frac{\sqrt{5}}{7^2})$ $\log_2 (\frac{\sqrt{5}}{49})$