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

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 $\ln$ . $\ln \sqrt [ 3 ] { \frac { a ^ { 9 } } { b ^ { 4 } } }$

A) $27 \mathrm { u } + 12 \mathrm { v }$
B) $27 u - 12 v$
C) $3 u - \frac { 4 } { 3 } v$
D) $9 u - 4 v$