Condense the expression to the logarithm of a single quantity. $2 [ 3 \ln x - \ln ( x + 8 ) - \ln ( x - 8 ) ]$
A) $\ln \left( \frac { x ^ { 3 } } { ( x - 8 ) ( x + 8 ) } \right) ^ { 2 }$
B) $\ln \left( \frac { x ^ { 3 } ( x + 8 ) } { ( x - 8 ) } \right) ^ { 2 }$
C) $\ln \left( \frac { x ^ { 3 } ( x - 8 ) } { ( x + 8 ) } \right) ^ { 2 }$
D) $\ln \left( \frac { ( x - 8 ) } { x ^ { 3 } ( x + 8 ) } \right) ^ { 2 }$
E) $\ln \left( \frac { ( x + 8 ) } { x ^ { 3 } ( x - 8 ) } \right) ^ { 2 }$

Question

Condense the expression to the logarithm of a single quantity.  $2 [ 3 \ln x - \ln ( x + 8 ) - \ln ( x - 8 ) ]$ 
A) $\ln \left( \frac { x ^ { 3 } } { ( x - 8 ) ( x + 8 ) } \right) ^ { 2 }$
B) $\ln \left( \frac { x ^ { 3 } ( x + 8 ) } { ( x - 8 ) } \right) ^ { 2 }$
C) $\ln \left( \frac { x ^ { 3 } ( x - 8 ) } { ( x + 8 ) } \right) ^ { 2 }$
D) $\ln \left( \frac { ( x - 8 ) } { x ^ { 3 } ( x + 8 ) } \right) ^ { 2 }$
E) $\ln \left( \frac { ( x + 8 ) } { x ^ { 3 } ( x - 8 ) } \right) ^ { 2 }$

Quizplus · Accepted Answer

Using logarithm properties, the expression can be simplified as follows: $2 [ 3 \ln x - \ln ( x + 8 ) - \ln ( x - 8 ) ] = 2 \ln \left( \frac{x^3}{(x+8)(x-8)} \right)$, which matches choice A when the exponent 2 is applied to the fraction inside the logarithm.

Condense the Expression to the Logarithm of a Single Quantity 2[3ln⁡x−ln⁡(x+8)−ln⁡(x−8)]2 [ 3 \ln x - \ln ( x + 8 ) - \ln ( x - 8 ) ]2[3lnx−ln(x+8)−ln(x−8)]

Condense the Expression to the Logarithm of a Single Quantity $2 [ 3 \ln x - \ln ( x + 8 ) - \ln ( x - 8 ) ]$