Write the following expression as a logarithm of a single quantity. $5 \ln x - 3 \ln \left( x ^ { 2 } + 3 \right)$
A) $\ln \left( \frac { x ^ { 5 } } { 3 \left( x ^ { 2 } + 3 \right) } \right)$
B) $\ln \left( \frac { x ^ { 5 } } { \left( x ^ { 2 } + 3 \right) ^ { 3 } } \right)$
C) $\ln \left( x ^ { 5 } - \left( x ^ { 2 } + 3 \right) ^ { 3 } \right)$
D) $\ln \left( 5 x - 3 \left( x ^ { 2 } + 3 \right) \right)$
E)none of the above

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties: $5 \ln x$ becomes $\ln(x^5)$ and $3 \ln(x^2 + 3)$ becomes $\ln((x^2 + 3)^3)$. Using the subtraction rule, $\ln a - \ln b = \ln(\frac{a}{b})$, the expression simplifies to $\ln \left( \frac { x ^ { 5 } } { \left( x ^ { 2 } + 3 \right) ^ { 3 } } \right)$.

Write the Following Expression as a Logarithm of a Single 5ln⁡x−3ln⁡(x2+3)5 \ln x - 3 \ln \left( x ^ { 2 } + 3 \right)5lnx−3ln(x2+3)

Write the Following Expression as a Logarithm of a Single $5 \ln x - 3 \ln \left( x ^ { 2 } + 3 \right)$