Condense the expression to the logarithm of a single quantity. $\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]$
A) $\ln \frac { ( x - 6 ) } { x ( x + 6 ) }$
B) $\ln \frac { ( x + 6 ) } { x ( x - 6 ) }$
C) $\ln \frac { x ( x - 6 ) } { ( x + 6 ) }$
D) $\ln \frac { x } { ( x - 6 ) ( x + 6 ) }$
E) $\ln \frac { x ( x + 6 ) } { ( x - 6 ) }$

Question

Condense the expression to the logarithm of a single quantity.  $\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]$ 
A) $\ln \frac { ( x - 6 ) } { x ( x + 6 ) }$
B) $\ln \frac { ( x + 6 ) } { x ( x - 6 ) }$
C) $\ln \frac { x ( x - 6 ) } { ( x + 6 ) }$
D) $\ln \frac { x } { ( x - 6 ) ( x + 6 ) }$
E) $\ln \frac { x ( x + 6 ) } { ( x - 6 ) }$

Quizplus · Accepted Answer

The expression simplifies using logarithm properties: $\ln x - \ln (x + 6) - \ln (x - 6) = \ln \frac{x}{(x + 6)(x - 6)}$, which matches choice D.

Condense the Expression to the Logarithm of a Single Quantity ln⁡x−[ln⁡(x+6)+ln⁡(x−6)]\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]lnx−[ln(x+6)+ln(x−6)]

Condense the Expression to the Logarithm of a Single Quantity $\ln x - [ \ln ( x + 6 ) + \ln ( x - 6 ) ]$