Use the properties of logarithms to write the expression $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$ as a sum, difference, or multiple of logarithms. Assume x and y are positive numbers. Simplify if possible.
A) $1 + \log _ { 4 } 9 x - \log _ { 4 } y$
B) $1 + 9 \log _ { 4 } x - \log _ { 4 } y$
C) $\log _ { 4 } 36 + \log _ { 4 } x - \log _ { 4 } y$
D) $\log _ { 4 } 1 + 9 \log _ { 4 } x + \log _ { 4 } y$

Question

Quizplus · Accepted Answer

The expression $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$ can be simplified using the properties of logarithms: the logarithm of a product is the sum of the logarithms, 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. Therefore, it simplifies to $1 + 9 \log _ { 4 } x - \log _ { 4 } y$.

Use the Properties of Logarithms to Write the Expression log⁡44x9y\log _ { 4 } \frac { 4 x ^ { 9 } } { y }log4​y4x9​

Use the Properties of Logarithms to Write the Expression $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$