Rewrite as a single logarithm.
-$2 \log _ { 2 } ( 2 x + 5 ) + 6 \log _ { 2 } ( 6 x + 1 )$
A) $\log _ { 2 } ( 2 x + 5 ) ^ { 2 } ( 6 x + 1 ) ^ { 6 }$
B) $12 \log _ { 2 } ( 2 x + 5 ) ( 6 x + 1 )$
C) $\log _ { 2 } \left( ( 2 x + 5 ) ^ { 2 } + ( 6 x + 1 ) ^ { 6 } \right)$
D) $\log _ { 2 } \frac { ( 2 x + 5 ) ^ { 2 } } { ( 6 x + 1 ) ^ { 6 } }$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to rewrite the expression as a single logarithm by applying the power rule, $\log_b(m^n) = n \log_b(m)$, and the product rule, $\log_b(m) + \log_b(n) = \log_b(mn)$, resulting in $\log_2((2x+5)^2(6x+1)^6)$.

Rewrite as a Single Logarithm 2log⁡2(2x+5)+6log⁡2(6x+1)2 \log _ { 2 } ( 2 x + 5 ) + 6 \log _ { 2 } ( 6 x + 1 )2log2​(2x+5)+6log2​(6x+1)

Rewrite as a Single Logarithm $2 \log _ { 2 } ( 2 x + 5 ) + 6 \log _ { 2 } ( 6 x + 1 )$