Condense the expression below to the logarithm of a single quantity.
$$\frac { 5 } { 2 } \log _ { 8 } ( z - 1 )$$
A) $\log _ { 8 } ( \sqrt [ 5 ] { z } - 1 )$
B) $\log _ { 8 } \left( \sqrt { z ^ { 5 } } - 1 \right)$
C) $\log _ { 8 } \sqrt [ 5 ] { z - 1 }$
D) $\log _ { 8 } \frac { 5 ( z - 1 ) } { 2 }$
E) $\log _ { 8 } \sqrt { ( z - 1 ) ^ { 5 } }$

Question

Quizplus · Accepted Answer

The expression can be simplified using the logarithm power rule, $\log_b(m^n) = n \log_b(m)$, which in this case gives $\log_8((z-1)^{5/2})$, equivalent to $\log_8 \sqrt{(z-1)^5}$.

Condense the Expression Below to the Logarithm of a Single 52log⁡8(z−1)\frac { 5 } { 2 } \log _ { 8 } ( z - 1 )25​log8​(z−1)

Condense the Expression Below to the Logarithm of a Single $\frac { 5 } { 2 } \log _ { 8 } ( z - 1 )$