Express as a single logarithm.
-$3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )$
A) $\log _ { 6 } x ( x - 6 )$
B) $\log _ { 6 } x ( x - 6 ) ^ { 15 }$
C) $15 \log _ { 6 } x ( x - 6 )$
D) $\log _ { 6 } x ^ { 3 } ( x - 6 ) ^ { 5 }$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to manipulate the expression as follows: $3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )$ can be rewritten using the power rule of logarithms ($m \log_b(x) = \log_b(x^m)$) as $\log _ { 6 } x^3 + \log _ { 6 } ( x - 6 )^5$. Then, using the product rule of logarithms ($\log_b(x) + \log_b(y) = \log_b(xy)$), we combine these into a single logarithm: $\log _ { 6 } x^3 ( x - 6 )^5$, which matches choice D.

Express as a Single Logarithm 3log⁡6x+5log⁡6(x−6)3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )3log6​x+5log6​(x−6)

Express as a Single Logarithm $3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )$