Solve the problem.
-Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$. Write the following expression in terms of $u$ and $\mathrm { v }$ without using the function $\ln$.
$\ln \left( b ^ { 4 } \sqrt [ 3 ] { a } \right)$
A) $4 \mathrm { v } + \frac { \mathrm { u } } { 3 }$
B) $4 \mathrm { v } + \frac { \mathrm { u } } { 4 }$
C) $4 \mathrm { v } - \frac { \mathrm { u } } { 3 }$
D) $4 \mathrm { v } + 3 \mathrm { u }$

Question

Quizplus · Accepted Answer

Using properties of logarithms, $\ln(b^4\sqrt[3]{a}) = \ln(b^4) + \ln(\sqrt[3]{a}) = 4\ln(b) + \frac{1}{3}\ln(a) = 4v + \frac{u}{3}$.

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

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