Solve the problem.
-Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$. Write the following expression in terms of $\mathrm { u }$ and $\mathrm { v }$ without using the function $\ln$.
$\ln \left( \sqrt [ 5 ] { a b ^ { 6 } } \right)$
A) $\frac { u } { 5 } + \frac { 6 } { 5 } v$
B) $\frac { \mathrm { u } } { 5 } - 6 \mathrm { v }$
C) $\frac { u } { 5 } - \frac { 6 } { 5 } v$
D) $\frac { 6 } { 5 } u + \frac { 6 } { 5 } v$

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties: $\ln \left( \sqrt [ 5 ] { a b ^ { 6 } } \right) = \ln \left( a^{1/5} b^{6/5} \right) = \frac{1}{5}\ln a + \frac{6}{5}\ln b = \frac{u}{5} + \frac{6v}{5}$.

Solve the Problem u=ln⁡a\mathrm { u } = \ln \mathrm { a }u=lna

Solve the Problem $\mathrm { u } = \ln \mathrm { a }$