Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
-$3 \log _ { 4 } ( 4 x - 2 ) + 6 \log _ { 4 } ( 2 x + 7 )$
A) $\log _ { 4 } \left( ( 4 x - 2 ) ^ { 3 } + ( 2 x + 7 ) ^ { 6 } \right)$
B) $\log _ { 4 } ( 4 x - 2 ) ^ { 3 } ( 2 x + 7 ) ^ { 6 }$
C) $18 \log _ { 4 } ( 4 x - 2 ) ( 2 x + 7 )$
D) $\log _ { 4 } \frac { ( 4 x - 2 ) ^ { 3 } } { ( 2 x + 7 ) ^ { 6 } }$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to write the sum of logarithms as the logarithm of the product of the arguments, and to move the coefficients inside the logarithms as exponents. Thus, $3 \log _ { 4 } ( 4 x - 2 ) + 6 \log _ { 4 } ( 2 x + 7 )$ becomes $\log _ { 4 } ( 4 x - 2 ) ^ { 3 } ( 2 x + 7 ) ^ { 6 }$.

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 $a \neq 1 \text { and } b \neq 1$