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. $\ln \left( b ^ { 2 } \sqrt [ 5 ] { a } \right)$
A) $2 \mathrm { v } = \frac { \mathrm { u } } { 5 }$
B) $2 \mathrm { v } + \frac { \mathrm { u } } { 2 }$
C) $2 v + 5 u$
D) $2 v + \frac { u } { 5 }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression $\ln \left( b ^ { 2 } \sqrt [ 5 ] { a } \right)$ can be rewritten as $2\ln(b) + \frac{1}{5}\ln(a)$, which translates to $2v + \frac{u}{5}$ based on the given substitutions.

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

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