Answer
$$\log_5 (\frac{2(x+1)}{(3x+7)^{\frac{1}{3}}})$$
Simplified:
$$\log_5 (\frac{2x+2}{(3x+7)^{\frac{1}{3}}})$$
Work Step by Step
$Combine$ $into$ $a$ $single$ $logarithm:$
$\log_5 2$ +$\log_5 (x+1)$ - $\frac{1}{3}\log_5 (3x+7)$
Use the First Law of Logarithms for $\log_5 2$ +$\log_5 (x+1)$
$\log_5 2$ +$\log_5 (x+1)$ = $\log_5 (2\times (x+1))$
$\log_5 2(x+1)$ - $\frac{1}{3}\log_5 (3x+7)$
Use the Third Law of Logarithms for $\frac{1}{3}\log_5 (3x+7)$
$\frac{1}{3}\log_5 (3x+7)$ = $\log_5 (3x+7)^{\frac{1}{3}}$
$\log_5 2(x+1)$ - $\log_5 (3x+7)^{\frac{1}{3}}$
Use the Second Law of Logarithms
$\log_5 2(x+1)$ - $\frac{1}{3}\log_5 (3x+7)$ = $\log_5 \frac{2(x+1)}{(3x+7)^{\frac{1}{3}}}$
$$\log_5 (\frac{2(x+1)}{(3x+7)^{\frac{1}{3}}})$$
Simplify if necessary
$$\log_5 (\frac{2x+2}{(3x+7)^{\frac{1}{3}}})$$
