Use properties of logarithms to evaluate the expression.
-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 funct $\ln \sqrt [ 3 ] { \frac { a ^ { 5 } } { b ^ { 7 } } }$
A) $15 u - 21 v$
B) $5 u - 7 v$
C) $\frac { 5 } { 3 } u - \frac { 7 } { 3 } v$
D) $15 u + 21 v$ n ln.286)

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties: $\ln \sqrt[3]{\frac{a^5}{b^7}} = \frac{1}{3} \ln \left(\frac{a^5}{b^7}\right) = \frac{1}{3} (\ln a^5 - \ln b^7) = \frac{1}{3} (5\ln a - 7\ln b) = \frac{5}{3}u - \frac{7}{3}v$.

Use Properties of Logarithms to Evaluate the Expression u=ln⁡a\mathrm { u } = \ln \mathrm { a }u=lna

Use Properties of Logarithms to Evaluate the Expression $\mathrm { u } = \ln \mathrm { a }$