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 $\ln$. $\ln \left( \sqrt [ 3 ] { a b ^ { 4 } } \right)$
A) $\frac { \mathrm { u } } { 3 } - \frac { 4 } { 3 } \mathrm { v }$
B) $\frac { u } { 3 } + \frac { 4 } { 3 } v$
C) $\frac { 4 } { 3 } u + \frac { 4 } { 3 } v$
D) $\frac { \mathrm { u } } { 3 } - 4 \mathrm { v }$

Question

Quizplus · Accepted Answer

The expression $\ln \left( \sqrt [ 3 ] { a b ^ { 4 } } \right)$ simplifies using logarithm properties: $\ln(a^{1/3}b^{4/3}) = \frac{1}{3}\ln(a) + \frac{4}{3}\ln(b) = \frac{u}{3} + \frac{4v}{3}$.

Let u=ln⁡a\mathrm { u } = \ln \mathrm { a }u=lna

Let $\mathrm { u } = \ln \mathrm { a }$