Provide an appropriate response.
-Write the expression $\log _ { 7 } \frac { 3 x } { y ^ { 2 } }$ as a sum or difference of logarithms.
A) $\log _ { 7 } 3 + \log _ { 7 } x - 2 \log _ { 7 } y$
B) $3 \log _ { 7 } x - 2 \log _ { 7 } y$
C) $2 \left( \log _ { 7 } 3 + \log _ { 7 } x - \log _ { 7 } y \right)$
D) $\log _ { 7 } 3 - \log _ { 7 } x + 2 \log _ { 7 } y$

Question

Quizplus · Accepted Answer

The expression $\log _ { 7 } \frac { 3 x } { y ^ { 2 } }$ can be broken down using logarithm properties: the logarithm of a product is the sum of the logarithms ($\log _ { 7 } 3 + \log _ { 7 } x$), and the logarithm of a quotient is the difference of the logarithms. Additionally, the exponent in the denominator becomes a coefficient in front of the logarithm ($- 2 \log _ { 7 } y$). Therefore, the correct expression is $\log _ { 7 } 3 + \log _ { 7 } x - 2 \log _ { 7 } y$.

Provide an Appropriate Response log⁡73xy2\log _ { 7 } \frac { 3 x } { y ^ { 2 } }log7​y23x​

Provide an Appropriate Response $\log _ { 7 } \frac { 3 x } { y ^ { 2 } }$