# How do you condense 2ln (2x+4) - Ln x - Ln 4 - Ln (x² + 4x + 4)?

May 3, 2016

$- \ln x$

#### Explanation:

Use $n \ln m = \ln \left({m}^{n}\right) \mathmr{and} \ln \left(\frac{1}{m}\right) = - \ln m .$.

The expression = $\ln \left(\frac{{\left(2 \left(x + 2\right)\right)}^{2}}{\left(x\right) \left(4\right) {\left(x + 2\right)}^{2}}\right)$.

Assume x > 0) and cancel common factors.

Now, it reduces to $\ln \left(\frac{1}{x}\right) = - \ln x$