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

Using the laws of logarithms, we can simplify the expression as:
$$4\ln 3 - \frac{3}{4}\ln(x+3) = \ln\left(3^4ight) - \ln\left((x+3)^{3/4}ight)$$
Now, we can further simplify this expression using the property $\ln(a^n) = n\ln(a)$:
$$\ln\left(3^4ight) - \ln\left((x+3)^{3/4}ight) = \ln\left(\frac{3^4}{(x+3)^{3/4}}ight) = \boxed{\ln\frac{81}{(x+3)^{3/4}}}	ext{, Answer A}$$

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