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.
-$6 \ln x - \frac { 1 } { 4 } \ln y$
A) $\ln \frac { x ^ { 6 } } { \sqrt [ 4 ] { y } }$
B) $\ln \frac { x ^ { 6 } } { y ^ { 4 } }$
C) $\ln x ^ { 6 } \sqrt [ 4 ] { y }$
D) $\ln x ^ { 6 } y ^ { 4 }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, specifically the power rule $\log_b(m^n) = n \log_b(m)$ and the quotient rule $\log_b \frac{m}{n} = \log_b m - \log_b n$, the expression can be condensed to $\ln \frac { x ^ { 6 } } { \sqrt [ 4 ] { y } }$.

Use Properties of Logarithms to Condense the Logarithmic Expression 6ln⁡x−14ln⁡y6 \ln x - \frac { 1 } { 4 } \ln y6lnx−41​lny

Use Properties of Logarithms to Condense the Logarithmic Expression $6 \ln x - \frac { 1 } { 4 } \ln y$