# How do you condense 1/2log_8(x+5)-3log_8(y)?

Apr 12, 2016

In this problem, the following log rules will be used:

#### Explanation:

$a \log n = \log {n}^{a}$

${\log}_{n} a - {\log}_{n} b = {\log}_{n} \left(\frac{a}{b}\right)$

Since ${x}^{\frac{1}{2}}$ = $\sqrt{x}$ (by the rule ${a}^{\frac{n}{m}} = \sqrt[n]{{a}^{m}}$):

${\log}_{8} \sqrt{x + 5} - {\log}_{8} \left({y}^{3}\right)$

${\log}_{8} \left(\frac{\sqrt{x + 5}}{{y}^{3}}\right)$