Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 5 } \frac { x ^ { 5 } } { y ^ { 8 } }$
A) $5 \log _ { 5 } x + 8 \log _ { 5 } y$
B) $5 \log _ { 5 } x - 8 \log _ { 5 } y$
C) $\frac { 5 } { 8 } \log _ { 5 } \frac { x } { y }$
D) $8 \log _ { 5 } y - 5 \log _ { 5 } x$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression $\log _ { 5 } \frac { x ^ { 5 } } { y ^ { 8 } }$ can be rewritten as $5 \log _ { 5 } x - 8 \log _ { 5 } y$, because the logarithm of a quotient is the difference of the logarithms, and the logarithm of a power is the exponent times the logarithm of the base.

Write the Expression as Sums or Differences of Multiples of Logarithms