Use the laws of logarithms to expand the expression. Select the correct answer.
$\ln \left( \frac { x + 5 } { x - 6 } \right) ^ { 1 / 2 }$
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 can use the following laws of logarithms:
1. $\ln(ab)=\ln a+\ln b$
2. $\ln\left(\frac{a}{b}\right)=\ln a-\ln b$
3. $\ln a^c=c\ln a$
Using these laws, we can rewrite the expression as:
$$\ln\left(\frac{x+5}{x-6}\right)^{1/2}=\frac{1}{2}\ln\left(\frac{x+5}{x-6}\right)$$
Therefore, the correct choice is D as it matches this result.

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 $\ln \left( \frac { x + 5 } { x - 6 } \right) ^ { 1 / 2 }$