Use the properties of logarithms to write $5 \log _ { 5 } ( x - 2 ) - \log _ { 5 } x$ as a single logarithm. Assume x is a positive number.
A) $\frac { \log _ { 5 } ( x - 2 ) ^ { 5 } } { \log _ { 5 } x }$
B) $\log _ { 5 } \frac { ( x - 2 ) ^ { 5 } } { x }$
C) $\log _ { 5 } x ( x - 2 ) ^ { 5 }$
D) $\log _ { 5 } \left( \frac { x - 2 } { x } \right) ^ { 5 }$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to combine the terms: $5 \log _ { 5 } ( x - 2 )$ can be rewritten as $\log _ { 5 } ( x - 2 ) ^ { 5 }$ using the power rule, and the subtraction can be turned into division, resulting in $\log _ { 5 } \frac { ( x - 2 ) ^ { 5 } } { x }$.

Use the Properties of Logarithms to Write 5log⁡5(x−2)−log⁡5x5 \log _ { 5 } ( x - 2 ) - \log _ { 5 } x5log5​(x−2)−log5​x

Use the Properties of Logarithms to Write $5 \log _ { 5 } ( x - 2 ) - \log _ { 5 } x$