# How do you condense ln3+1/3ln(4 - x^2) - ln x ?

Jul 16, 2016

=$\ln \left[\frac{3 {\left(4 - {x}^{2}\right)}^{\frac{1}{3}}}{x}\right]$ or it can be written as

$\ln \left[\frac{3 \times \sqrt[3]{4 - {x}^{2}}}{x}\right]$

#### Explanation:

If logs are added, the numbers are multiplied.
If logs are subtracted, the numbers are divided.

$\ln 3 + \frac{1}{3} \ln \left(4 - {x}^{2}\right) - \ln x$

=$\ln 3 + \ln {\left(4 - {x}^{2}\right)}^{\frac{1}{3}} - \ln x \text{ power law}$

=$\ln \left[\frac{3 {\left(4 - {x}^{2}\right)}^{\frac{1}{3}}}{x}\right]$

or it can be written as

$\ln \left[\frac{3 \times \sqrt[3]{4 - {x}^{2}}}{x}\right]$