Answer
$\log_2 (\frac{\sqrt{5}}{49})$
Work Step by Step
$Combine$ $the$ $expression$:
$\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
$\log_2 \sqrt{5}$ - $\log_2 7^2$ = $\log_2 (\frac{\sqrt{5}}{7^2})$
$\log_2 (\frac{\sqrt{5}}{49})$
