Use the laws of logarithms to write the expression as the logarithm of a single quantity.
$4 \ln 3 - \frac { 3 } { 4 } \ln ( x + 3 )$
A) $\ln \frac { 81 } { ( x + 3 ) ^ { 3 / 4 } }$
B) $\frac { 3 \ln 81 } { 4 ( x + 3 ) }$
C) $\ln 3 ^ { 4 } - \ln ( x + 3 ) ^ { 3 / 4 }$
D) $\frac { 4 \ln 3 } { \frac { 3 } { 4 } \ln ( x + 3 ) }$

Question

Quizplus · Accepted Answer

We use the laws of logarithms to bring the expression into a single logarithm:
$$4 \ln 3 - \frac{ 3 }{ 4 } \ln ( x + 3 ) = \ln ( 3^4 ) - \ln ( x + 3 ) ^ { 3 / 4 }$$
$$\ln \frac { 3^4 } { ( x + 3 ) ^ { 3 / 4 } } = \ln \frac { 81 } { ( x + 3 ) ^ { 3 / 4 } }$$ Therefore, the answer is A.

Use the Laws of Logarithms to Write the Expression as the Logarithm