Condense the expression below to the logarithm of a single quantity.
$$\frac { 3 } { 2 } \log _ { 7 } ( z + 5 )$$
A) $\log _ { 7 } ( \sqrt [ 3 ] { z } + 5 )$
B) $\log _ { 7 } \left( \sqrt { z ^ { 3 } } + 5 \right)$
C) $\log _ { 7 } \sqrt [ 3 ] { z + 5 }$
D) $\log _ { 7 } \frac { 3 ( z + 5 ) } { 2 }$
E) $\quad \log _ { 7 } \sqrt { ( z + 5 ) ^ { 3 } }$

Question

Quizplus · Accepted Answer

The correct answer is $\log _ { 7 } \sqrt { ( z + 5 ) ^ { 3 } }$ because the coefficient $\frac { 3 } { 2 }$ in front of the logarithm can be moved inside the logarithm as the exponent of the argument, resulting in the cube of $z + 5$ inside the square root.

Condense the Expression Below to the Logarithm of a Single 32log⁡7(z+5)\frac { 3 } { 2 } \log _ { 7 } ( z + 5 )23​log7​(z+5)

Condense the Expression Below to the Logarithm of a Single $\frac { 3 } { 2 } \log _ { 7 } ( z + 5 )$