Write the Logarithm as a Sum or Difference of Logarithms $$\ln \left[ \frac { 5 x \left( x ^ { 9 } + 4 \right) ^ { 9 } } { \sqrt [ 9 ] { 3 + 5 x } } \right]$$

Multiple Choice

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
- $$\ln \left[ \frac { 5 x \left( x ^ { 9 } + 4 \right) ^ { 9 } } { \sqrt [ 9 ] { 3 + 5 x } } \right]$$

A) $\ln 5 x + 9 \ln \left( x ^ { 9 } + 4 - \frac { 1 } { 9 } \ln 3 + 5 x \right)$
B) $\ln 5 + \ln x + 9 \ln \left( x ^ { 9 } + 4 \right) - \frac { 1 } { 9 } \ln ( 3 + 5 x )$
C) $\ln 5 + \ln x + 81 \ln x + 9 \ln 4 - \frac { 1 } { 9 } \ln 3 - \frac { 1 } { 9 } \ln 5 - \frac { 1 } { 9 } \ln x$
D) $\ln 5 + \ln x + 729 \ln x \cdot \ln 4 - \frac { 1 } { 81 } \ln 3 \cdot \ln 5 - \frac { 1 } { 81 } \ln 3 \cdot \ln x$