Answer
$$\ln \sqrt {(x-4)(x^2+4x)^5}$$
Work Step by Step
$Combine$ $into$ $a$ $single$ $logarithm:$
$\frac{1}{2}[\ln (x-4) + 5\ln (x^2+4x)]$
Use the Third Law of Logarithms
$\frac{1}{2}[\ln (x-4) + 5\ln (x^2+4x)]$ = $[\ln (x-4) + 5\ln (x^2+4x)]^{\frac{1}{2}}$
Use the Third Law of Logarithms for $5\ln (x^2+4x)$
$5\ln (x^2+4x)$ = $\ln (x^2+4x)^5$
$[\ln (x-4) + \ln (x^2+4x)^5]^{\frac{1}{2}}$
Use the First Law of Logarithms inside the brackets
$\ln (x-4) + \ln (x^2+4x)^5$ = $\ln ((x-4)(x^2+4x)^5)$
$\ln ((x-4)(x^2+4x)^5)^{\frac{1}{2}}$
Simplify
$$\ln \sqrt {(x-4)(x^2+4x)^5}$$
