Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
-$\log _ { 6 } x ^ { 4 } y ^ { 5 }$
A) $20 \log _ { 6 } x + 20 \log _ { 6 } y$
B) $\log _ { 6 } x ^ { 4 } + \log _ { 6 } y ^ { 5 }$
C) $9 \left( \log _ { 6 } x + \log _ { 6 } y \right)$
D) $4 \log _ { 6 } x + 5 \log _ { 6 } y$

Question

Quizplus · Accepted Answer

The logarithm of a product can be written as the sum of the logarithms of its factors, and the logarithm of a power can be distributed as the exponent times the logarithm of the base. Therefore, $\log _ { 6 } x ^ { 4 } y ^ { 5 }$ simplifies to $4 \log _ { 6 } x + 5 \log _ { 6 } y$.

Write the Logarithm as a Sum or Difference of Logarithms log⁡6x4y5\log _ { 6 } x ^ { 4 } y ^ { 5 }log6​x4y5

Write the Logarithm as a Sum or Difference of Logarithms $\log _ { 6 } x ^ { 4 } y ^ { 5 }$