Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $$a \neq 1 \text { and } b \neq 1$$
-$2 \log _ { 6 } ( 3 x - 3 ) + 6 \log _ { 6 } ( 2 x + 1 )$
A) $\log _ { 6 } \left( ( 3 x - 3 ) ^ { 2 } + ( 2 x + 1 ) ^ { 6 } \right)$
B) $\log _ { 6 } \frac { ( 3 x - 3 ) ^ { 2 } } { ( 2 x + 1 ) ^ { 6 } }$
C) $\log _ { 6 } ( 3 x - 3 ) ^ { 2 } ( 2 x + 1 ) ^ { 6 }$
D) $12 \log _ { 6 } ( 3 x - 3 ) ( 2 x + 1 )$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to manipulate the expression: the coefficient in front of a logarithm can be moved as an exponent of its argument, and the sum of logarithms with the same base can be written as the logarithm of the product of their arguments. Thus, $2 \log _ { 6 } ( 3 x - 3 ) + 6 \log _ { 6 } ( 2 x + 1 )$ becomes $\log _ { 6 } ( 3 x - 3 ) ^ { 2 } ( 2 x + 1 ) ^ { 6 }$.

Write the Expression as a Single Logarithm with Coefficient 1 a≠1 and b≠1a \neq 1 \text { and } b \neq 1a=1 and b=1

Write the Expression as a Single Logarithm with Coefficient 1 $a \neq 1 \text { and } b \neq 1$