Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
$\ln \sqrt [ 4 ] { t }$
A) $\frac { 1 } { 4 } \ln t$
B) $\ln t - \frac { 1 } { 4 }$
C) $\ln t - 4$
D) $\frac { 1 } { 2 } \ln t$
E) $\ln t - \frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

We can use the property of logarithms that states that $\log_ab^c=c\log_ab$ to rewrite the expression as $\ln(t^{1/4})=\frac{1}{4}\ln t$. Therefore, the best choice is A.

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