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

Question

Quizplus · Accepted Answer

Using the logarithm properties, $\log_b \frac{M}{N} = \log_b M - \log_b N$ and $\log_b M^n = n \log_b M$, the expression $\log_5 \frac{x - 3}{x^3}$ can be rewritten as $\log_5 (x - 3) - \log_5 x^3$, which simplifies further to $\log_5 (x - 3) - 3\log_5 x$.

Write the Expression as Sums or Differences of Multiples of Logarithms