Solve the problem.
-Let $u = \ln a$ and $v = \ln b$. Write the following expression in terms of $u$ and $v$ without using the function $\ln$.
$\ln \sqrt [ 3 ] { \frac { a ^ { 6 } } { b ^ { 9 } } }$
A) $18 u - 27 v$
B) $6 u - 9 v$
C) $2 u - 3 v$
D) $18 u + 27 v$

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties: $\ln \sqrt [ 3 ] { \frac { a ^ { 6 } } { b ^ { 9 } } } = \frac { 1 } { 3 } \ln \left( a ^ { 6 } / b ^ { 9 } \right) = \frac { 1 } { 3 } (6 \ln a - 9 \ln b) = 2 \ln a - 3 \ln b = 2u - 3v$.

Solve the Problem u=ln⁡au = \ln au=lna And v=ln⁡bv = \ln bv=lnb

Solve the Problem $u = \ln a$ And $v = \ln b$