Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$$5 \ln ( x - 11 ) - 8 \ln x$$
A) $\ln \frac { 5 ( x - 11 ) } { 8 x }$
B) $\ln 40 x ( x - 11 )$
C) $\ln x ^ { 8 } ( x - 11 ) ^ { 5 }$
D) $\ln \frac { ( x - 11 ) ^ { 5 } } { x ^ { 8 } }$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to condense the expression by combining the logarithms and using the power rule. The correct answer is $\ln \frac { ( x - 11 ) ^ { 5 } } { x ^ { 8 } }$, which uses the property that $a \ln b = \ln b^a$ and the quotient rule for logarithms.

Use Properties of Logarithms to Condense the Logarithmic Expression 5ln⁡(x−11)−8ln⁡x5 \ln ( x - 11 ) - 8 \ln x5ln(x−11)−8lnx

Use Properties of Logarithms to Condense the Logarithmic Expression $5 \ln ( x - 11 ) - 8 \ln x$