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

Using the logarithm power rule, $a \log_b(c) = \log_b(c^a)$, the expression can be rewritten as $\log_6 x^3 + \log_6 (x-6)^5$, which then combines into $\log_6 x^3(x-6)^5$ by the product rule for logarithms.

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 $3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )$