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

Question

Quizplus · Accepted Answer

The expression can be expanded using the power rule and the quotient rule of logarithms: $\ln\left(\frac{a}{b}\right) = \ln(a) - \ln(b)$ and $\ln(a^b) = b \cdot \ln(a)$.

Use the Laws of Logarithms to Expand the Expression (x+5x−6)12\left(\frac{x+5}{x-6}\right)^{\frac{1}{2}}(x−6x+5​)21​ A) 12\frac{1}{2}21​

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