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.
-$3 \ln ( x - 6 ) - 10 \ln x$
A) $\ln \frac { ( x - 6 ) ^ { 3 } } { x ^ { 10 } }$
B) $\ln x ^ { 10 } ( x - 6 ) ^ { 3 }$
C) $\ln \frac { 3 ( x - 6 ) } { 10 x }$
D) $\ln 30 x ( x - 6 )$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression $3 \ln ( x - 6 ) - 10 \ln x$ can be rewritten as $\ln ( x - 6 )^3 - \ln x^{10}$, which simplifies to $\ln \frac { ( x - 6 ) ^ { 3 } } { x ^ { 10 } }$ by the quotient rule of logarithms.

Use Properties of Logarithms to Condense the Logarithmic Expression 3ln⁡(x−6)−10ln⁡x3 \ln ( x - 6 ) - 10 \ln x3ln(x−6)−10lnx

Use Properties of Logarithms to Condense the Logarithmic Expression $3 \ln ( x - 6 ) - 10 \ln x$