Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 7 } x ^ { 3 } y ^ { 5 }$
A) $8 + \log _ { 7 } x + \log _ { 3 } y$
B) $3 \log _ { 7 } x + 5 \log _ { 7 } y$
C) $15 \log _ { 7 } x + \log _ { 7 } y$
D) $3 \log _ { 7 } x - 5 \log _ { 7 } y$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to write the expression $\log_7 x^3y^5$ as a sum of multiples of logarithms: $3\log_7 x + 5\log_7 y$. This uses the property that $\log_b (M^k) = k\log_b M$ and $\log_b (MN) = \log_b M + \log_b N$.

Write the Expression as Sums or Differences of Multiples of Logarithms