Write the following expression as a logarithm of a single quantity. $\ln x - 16 \ln \left( x ^ { 2 } + 1 \right)$
A) $\ln \left( \frac { - 16 x } { \left( x ^ { 2 } + 1 \right) } \right)$
B) $\ln \left( \frac { x } { 16 \left( x ^ { 2 } + 1 \right) } \right)$
C) $\ln \left( x - 16 \left( x ^ { 2 } + 1 \right) \right)$
D) $\ln \left( \frac { x } { \left( x ^ { 2 } + 1 \right) ^ { 16 } } \right)$
E) $\ln \left( \frac { - 16 x } { x ^ { 2 } + 1 } \right)$

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties: $\ln a - \ln b = \ln \left( \frac{a}{b} \right)$ and $\ln a^n = n \ln a$. Applying these, we get $\ln x - 16 \ln \left( x^2 + 1 \right) = \ln \left( \frac{x}{\left( x^2 + 1 \right)^{16}} \right)$.

Write the Following Expression as a Logarithm of a Single ln⁡x−16ln⁡(x2+1)\ln x - 16 \ln \left( x ^ { 2 } + 1 \right)lnx−16ln(x2+1)

Write the Following Expression as a Logarithm of a Single $\ln x - 16 \ln \left( x ^ { 2 } + 1 \right)$