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.
-$$8 \ln ( x - 6 ) - 11 \ln x$$
A) $\ln \frac { ( x - 6 ) ^ { 8 } } { x ^ { 11 } }$
B) $\ln x ^ { 11 } ( x - 6 ) ^ { 8 }$
C) $\ln \frac { 8 ( x - 6 ) } { 11 x }$
D) $\ln 88 x ( x - 6 )$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can condense the expression as follows:
$$8\ln(x-6)-11\ln x = \ln((x-6)^8) - \ln(x^{11}) = \ln\left(\frac{(x-6)^8}{x^{11}}\right)$$

Use Properties of Logarithms to Condense the Logarithmic Expression 8ln⁡(x−6)−11ln⁡x8 \ln ( x - 6 ) - 11 \ln x8ln(x−6)−11lnx

Use Properties of Logarithms to Condense the Logarithmic Expression $8 \ln ( x - 6 ) - 11 \ln x$