# How do you write as a single logarithm Log_b 5 +1/3 Log_bx?

Jul 20, 2015

I found: ${\log}_{b} \left(5 {x}^{\frac{1}{3}}\right) = {\log}_{b} \left(5 \sqrt[3]{x}\right)$

#### Explanation:

You can use the fact that:
$a \log x = \log {x}^{a}$
and:
$\log a + \log b = \log \left(a \times b\right)$
So you get:
${\log}_{b} \left(5\right) + {\log}_{b} \left({x}^{\frac{1}{3}}\right) =$
$= {\log}_{b} \left(5 {x}^{\frac{1}{3}}\right)$