# How do you use the properties of logarithms to expand ln (6/sqrt(x^2+1))?

May 25, 2017

$\ln 6 - \frac{1}{2} \ln \left({x}^{2} + 1\right)$

#### Explanation:

Expand $\ln \left(\frac{6}{\sqrt{{x}^{2} + 1}}\right)$

Rewrite the square root as an exponent.

$\ln \left(\frac{6}{{x}^{2} + 1} ^ \left(\frac{1}{2}\right)\right)$

Use the log property $\log \left(\frac{a}{b}\right) = \log a - \log b$

$\ln 6 - \ln {\left({x}^{2} + 1\right)}^{\frac{1}{2}}$

Use the log property $\log {a}^{b} = b \log a$

$\ln 6 - \frac{1}{2} \ln \left({x}^{2} + 1\right)$