Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers.
-$4 \log _ { 4 } ( 6 x - 2 ) + 6 \log _ { 4 } ( 2 x - 4 )$
A) $\log _ { 4 } \left( ( 6 x - 2 ) ^ { 4 } + ( 2 x - 4 ) ^ { 6 } \right)$
B) $24 \log _ { 4 } ( 6 x - 2 ) ( 2 x - 4 )$
C) $\log _ { 4 } ( 6 x - 2 ) ^ { 4 } ( 2 x - 4 ) ^ { 6 }$
D) $\log _ { 4 } \frac { ( 6 x - 2 ) ^ { 4 } } { ( 2 x - 4 ) ^ { 6 } }$

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 to the exponent. Therefore, $4 \log _ { 4 } ( 6 x - 2 ) + 6 \log _ { 4 } ( 2 x - 4 )$ becomes $\log _ { 4 } ( 6 x - 2 ) ^ { 4 } ( 2 x - 4 ) ^ { 6 }$.

Write the Expression as a Single Logarithm with Coefficient 1 4log⁡4(6x−2)+6log⁡4(2x−4)4 \log _ { 4 } ( 6 x - 2 ) + 6 \log _ { 4 } ( 2 x - 4 )4log4​(6x−2)+6log4​(2x−4)

Write the Expression as a Single Logarithm with Coefficient 1 $4 \log _ { 4 } ( 6 x - 2 ) + 6 \log _ { 4 } ( 2 x - 4 )$