# How do you condense log_(6)(x+4)+1/2log_(6)x?

Aug 4, 2016

${\log}_{6} \left(\left(x + 4\right) \sqrt{x}\right)$

#### Explanation:

Since $n {\log}_{b} a = {\log}_{b} {a}^{n}$, you have

$\frac{1}{2} {\log}_{6} x = {\log}_{6} {x}^{\frac{1}{2}} = {\log}_{6} \sqrt{x}$

Since ${\log}_{b} a + {\log}_{b} c = {\log}_{b} \left(a c\right)$, you have

${\log}_{6} \left(x + 4\right) + {\log}_{6} \sqrt{x} = {\log}_{6} \left(\left(x + 4\right) \sqrt{x}\right)$