Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $\ln \sqrt [ 6 ] { t }$
A) $\frac { 1 } { 6 } \ln t$
B) $\ln t - \frac { 1 } { 6 }$
C) $\ln t - 6$
D) $\frac { 1 } { 3 } \ln t$
E) $\ln t - \frac { 1 } { 3 }$

Question

Quizplus · Accepted Answer

We can use the property $\log_b\sqrt[n]{x}=\frac{1}{n}\log_b x$ to rewrite the expression as $\ln(t^{1/6})=\frac{1}{6}\ln t$. Therefore, the answer is choice A.

Use the Properties of Logarithms to Expand the Expression as a Sum