Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 5 } \frac { x + 6 } { x ^ { 3 } }$
A) $\log _ { 5 } ( x + 6 ) - 3 \log _ { 5 } x$
B) $3 \log _ { 5 } x - \log _ { 5 } ( x + 6 )$
C) $\log _ { 5 } ( x + 6 ) + 3 \log _ { 5 } x$
D) $\log _ { 5 } ( x + 6 ) - \log _ { 5 } x$

Question

Quizplus · Accepted Answer

The expression can be rewritten using the logarithm properties: $\log_b \frac{M}{N} = \log_b M - \log_b N$ and $\log_b M^n = n \log_b M$. Thus, $\log_5 \frac{x + 6}{x^3} = \log_5 (x + 6) - \log_5 x^3 = \log_5 (x + 6) - 3\log_5 x$.

Write the Expression as Sums or Differences of Multiples of Logarithms