College Algebra 7th Edition

$\log_2{\left(\frac{\sqrt{5}}{49}\right)}$
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: $=\log_2{\left(\frac{\sqrt{5}}{49}\right)}$