Write the expression $3 \ln ( 2 ) - \frac { 1 } { 5 } \ln \left( x ^ { 2 } + 4 \right)$ as the logarithm of a single quantity.
A) $\ln \left[ \frac { 8 } { \left( x ^ { 2 } + 4 \right) ^ { 5 } } \right]$
B) $\ln \left( 8 \sqrt [ 5 ] { x ^ { 2 } + 4 } \right)$
C) $\ln \left[ \frac { 9 } { \sqrt [ 5 ] { x ^ { 2 } + 4 } } \right]$
D) $\ln \left( 9 \sqrt [ 5 ] { x ^ { 2 } + 4 } \right)$
E) $\ln \left[ \frac { 8 } { \sqrt [ 5 ] { x ^ { 2 } + 4 } } \right]$

Question

Quizplus · Accepted Answer

The expression can be rewritten using logarithm properties: $3 \ln(2) = \ln(2^3) = \ln(8)$ and $-\frac{1}{5} \ln(x^2 + 4) = \ln((x^2 + 4)^{-1/5})$. Combining these gives $\ln\left(\frac{8}{(x^2 + 4)^{1/5}}\right)$.

Write the Expression 3ln⁡(2)−15ln⁡(x2+4)3 \ln ( 2 ) - \frac { 1 } { 5 } \ln \left( x ^ { 2 } + 4 \right)3ln(2)−51​ln(x2+4)

Write the Expression $3 \ln ( 2 ) - \frac { 1 } { 5 } \ln \left( x ^ { 2 } + 4 \right)$