# How do you rewrite 2lnx+1/2lnu as a single log?

Jul 23, 2015

I found: $\ln \left({x}^{2} \sqrt{u}\right)$

#### Explanation:

Here you can use two properties of the logs:
1] $a \log x = \log {x}^{a}$
2] ${\log}_{b} x + {\log}_{b} y = {\log}_{b} \left(x \cdot y\right)$ (same base!)

So, in your case you get:
$\ln {x}^{2} + \ln {u}^{\frac{1}{2}} = \ln {x}^{2} + \ln \sqrt{u} =$ same base:
$= \ln \left({x}^{2} \sqrt{u}\right)$