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 following laws of logarithms:
1) $\ln a - \ln b = \ln \frac{a}{b}$
2) $\ln a^b = b \ln a$
Therefore, we can rewrite the expression as:
$4 \ln 3 - \frac{3}{4} \ln (x + 3) = \ln 3^4 - \ln (x + 3)^{3/4}$
Then, using law 1, we get:
$\ln \frac{3^4}{(x+3)^{3/4}} = \ln \frac{81}{(x+3)^{3/4}}$
So the answer is A.

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