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 can use the laws of logarithms to simplify the expression as follows:
\begin{align*}
4 \ln 3 - \frac{3}{4} \ln (x+3) &= \ln 3^4 - \ln (x+3)^{3/4} \
&= \ln \left( \frac{3^4}{(x+3)^{3/4}} ight) \
&= \ln \frac{81}{(x+3)^{3/4}}
\end{align*}
Therefore, the answer is choice A.

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