Express as a single logarithm.
-$3 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 2$
A) $\log _ { a } 2 ( x + 1 )$
B) $\log _ { a } ( 2 x + 1 ) + 2$
C) $\log _ { a } ( 2 x + 3 )$
D) $\log _ { a } \frac { a ^ { 2 } ( 2 x + 1 ) ^ { 3 } } { ( 2 x - 1 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

Using logarithm properties, the expression can be simplified to $\log_a \left( \frac{(2x+1)^3}{(2x-1)^2} \right)^2$, which simplifies further to $\log_a \frac{a^2(2x+1)^3}{(2x-1)^2}$, matching option D.

Express as a Single Logarithm 3log⁡a(2x+1)−2log⁡a(2x−1)+23 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 23loga​(2x+1)−2loga​(2x−1)+2

Express as a Single Logarithm $3 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 2$