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 $\ln$.
$\ln \frac { a ^ { 7 } } { b ^ { 2 } }$
A) $7 u + 2 v$
B) $u ^ { 7 } - v ^ { 2 }$
C) $7 \mathrm { u } - 2 \mathrm { v }$
D) $2 \mathrm { u } - 7 \mathrm { v }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, $\ln \frac { a ^ { 7 } } { b ^ { 2 } }$ simplifies to $7\ln a - 2\ln b$, which is $7u - 2v$ according to the given definitions of $u$ and $v$.

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

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