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.
-$8 \ln x - \frac { 1 } { 3 } \ln y$
A) $\ln \frac { x ^ { 8 } } { y ^ { 3 } }$
B) $\ln x ^ { 8 } y ^ { 3 }$
C) $\ln x ^ { 8 } \sqrt [ 3 ] { y }$
D) $\ln \frac { x ^ { 8 } } { \sqrt [ 3 ] { y } }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, $8 \ln x$ can be rewritten as $\ln x^8$ and $-\frac{1}{3} \ln y$ as $-\ln y^{\frac{1}{3}}$ or $\ln \frac{1}{y^{\frac{1}{3}}}$. Combining these gives $\ln \frac{x^8}{y^{\frac{1}{3}}}$ or $\ln \frac{x^8}{\sqrt[3]{y}}$.

Use Properties of Logarithms to Condense the Logarithmic Expression 8ln⁡x−13ln⁡y8 \ln x - \frac { 1 } { 3 } \ln y8lnx−31​lny

Use Properties of Logarithms to Condense the Logarithmic Expression $8 \ln x - \frac { 1 } { 3 } \ln y$