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) $\log _ { 7 } \sqrt { ( z + 5 ) ^ { 3 } }$

Question

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) $\log _ { 7 } \sqrt { ( z + 5 ) ^ { 3 } }$

Quizplus · Accepted Answer

The expression $\frac { 3 } { 2 } \log _ { 7 } ( z + 5 )$ can be rewritten using the logarithm power rule as $\log _ { 7 } ( z + 5 )^{3/2}$, which simplifies to $\log _ { 7 } \sqrt { ( z + 5 ) ^ { 3 } }$.

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 $\frac { 3 } { 2 } \log _ { 7 } ( z + 5 )$