Use the laws of logarithms to expand the expression.
$\ln \left( \frac { x + 5 } { x - 6 } \right) ^ { 1 / 2 }$
A) $\frac { 1 } { 2 } \ln \left( \frac { x + 5 } { x - 6 } \right)$
B) $\frac { 1 } { 2 } \ln [ ( x + 5 ) ( x - 6 ) ]$
C) $\frac { 1 } { 2 } \ln \left( x - \frac { 5 } { 6 } \right)$
D) $\frac { 1 } { 2 } \ln ( x + 5 ) - \frac { 1 } { 2 } \ln ( x - 6 )$

Question

Quizplus · Accepted Answer

We use the power rule of logarithms to take the exponent of 1/2 down as a coefficient. Then we use the quotient rule of logarithms to separate the logarithmic expression into two terms that are subtracted from each other. Therefore, 
\begin{align*}
\ln \left( \frac { x + 5 } { x - 6 } ight) ^ { 1 / 2 } &= \frac{1}{2} \ln \left( \frac { x + 5 } { x - 6 } ight) \
&= \frac{1}{2} [ \ln (x + 5) - \ln(x - 6) ] \
&= \frac{1}{2} \ln (x + 5) - \frac{1}{2} \ln(x - 6),
\end{align*}
which is option D.

Use the Laws of Logarithms to Expand the Expression ln⁡(x+5x−6)1/2\ln \left( \frac { x + 5 } { x - 6 } \right) ^ { 1 / 2 }ln(x−6x+5​)1/2

Use the Laws of Logarithms to Expand the Expression $\ln \left( \frac { x + 5 } { x - 6 } \right) ^ { 1 / 2 }$