# How do you expand ln(x/sqrt(x^6+3))?

Sep 4, 2016

The expression can be simplified to $\ln x - \frac{1}{2} \ln \left({x}^{6} + 3\right)$

#### Explanation:

Start by applying the rule ${\log}_{a} \left(\frac{n}{m}\right) = {\log}_{a} \left(n\right) - {\log}_{a} \left(m\right)$.

$\implies \ln \left(x\right) - \ln \left(\sqrt{{x}^{6} + 3}\right)$

Write the √ in exponential form.

$\implies \ln x - \ln {\left({x}^{6} + 3\right)}^{\frac{1}{2}}$

Now, use the rule $\log \left({a}^{n}\right) = n \log a$.

$\implies \ln x - \frac{1}{2} \ln \left({x}^{6} + 3\right)$

This is as far as we can go.

Hopefully this helps!