Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )$
A) $\log _ { 6 } x ^ { 3 } ( x - 6 ) ^ { 5 }$
B) $\log _ { 6 } x ( x - 6 ) ^ { 15 }$
C) $15 \log _ { 6 } x ( x - 6 )$
D) $\log _ { 6 } x ( x - 6 )$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, specifically the power rule $\log_b(m^n) = n \log_b(m)$, the given expression can be rewritten as a single logarithm: $\log_6 x^3 + \log_6 (x - 6)^5$. Then, applying the product rule $\log_b(m) + \log_b(n) = \log_b(mn)$, the expression becomes $\log_6 x^3(x - 6)^5$.

Use Properties of Logarithms to Condense the Logarithmic Expression 3log⁡6x+5log⁡6(x−6)3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )3log6​x+5log6​(x−6)

Use Properties of Logarithms to Condense the Logarithmic Expression $3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )$