Evaluate log base 12 of (x^4 square root of x^3-2)/((x+1)^5)

$\log_{12} (\frac{x^{4} \sqrt{x^{3} - 2}}{{(x + 1)}^{5}})$

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (\frac{x^{4} \sqrt{x^{3} - 2}}{{(x + 1)}^{5}})}{\log (12)}$