# How do you write as a single logarithm 1/2 Log _b3 +1/2 Log_bx - 3 Log_b Z?

Mar 15, 2018

${\log}_{b} \left(\frac{\sqrt{3 x}}{Z} ^ 3\right)$

#### Explanation:

Since $x \log y = \log {y}^{x}$, we can write:

${\log}_{b} \sqrt{3} + {\log}_{b} \sqrt{x} - {\log}_{b} {Z}^{3}$

Since $\log a + \log b = \log \left(a b\right)$, we write:

${\log}_{b} \sqrt{3 x} - {\log}_{b} {Z}^{3}$

Since $\log a - \log b = \log \left(\frac{a}{b}\right)$, we can write:

${\log}_{b} \left(\frac{\sqrt{3 x}}{Z} ^ 3\right)$