Answer
$\log_2{\left(\frac{\sqrt{5}}{49}\right)}$
Work Step by Step
RECALL:
(1) $\log_b{P} + \log_b{Q} = \log_b{(PQ)}$
(2) $\log_b{P} - \log_b{Q} = \log_b{(\frac{P}{Q})}$
(3) $a(\log_b{x}) = \log_b{(x^a)}$
Use rule (3) above to obtain:
$=\log_2{(5^{\frac{1}{2}})}-\log_2{(7^2)}
\\=\log_2{(5^{\frac{1}{2}})}-\log_2{49}$
Write $5^{\frac{1}{2}}$ as $\sqrt{5}$ to obtain:
$=\log_2{\sqrt{5}}-\log_2{49}$
Use rule (2) above to obtain:
$=\log_2{\left(\frac{\sqrt{5}}{49}\right)}$
