Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$2 \ln a - 9 \ln b$
A) $\ln \frac { a ^ { 2 } } { b ^ { 9 } }$
B) $\frac { \ln a ^ { 2 } } { \ln b ^ { 9 } }$
C) $\ln \left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { 11 }$
D) $\ln \frac { 2 a } { 9 b }$

Question

Quizplus · Accepted Answer

We can use the properties of logarithms that state:

1. $\log_a {x} - \log_a {y}=\log_a {\frac{x}{y}}$
2. $n\log_a {x}=\log_a {x^n}$

Using these properties, we can rewrite the expression as:

$2\ln{a} - 9\ln{b}=\ln{a^2}-\ln{b^9}=\ln{\frac{a^2}{b^9}}$

Therefore, the answer is choice A.

Use Properties of Logarithms to Condense the Logarithmic Expression 2ln⁡a−9ln⁡b2 \ln a - 9 \ln b2lna−9lnb

Use Properties of Logarithms to Condense the Logarithmic Expression $2 \ln a - 9 \ln b$