Use the properties of logarithms to write $\ln \frac { x } { \sqrt [ 3 ] { z } }$ as a sum, difference, or product of logarithms. Assume x and z are positive numbers.
A) $\ln x + \frac { 1 } { 3 } \ln z$
B) $\ln x - \frac { 1 } { 3 } \ln z$
C) $\ln x - 3 \ln z$
D) $\ln x + 3 \ln z$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression $\ln \frac { x } { \sqrt [ 3 ] { z } }$ can be rewritten as $\ln x - \ln (\sqrt[3]{z})$. Since $\ln (\sqrt[3]{z}) = \frac{1}{3} \ln z$, the expression simplifies to $\ln x - \frac { 1 } { 3 } \ln z$.

Use the Properties of Logarithms to Write ln⁡xz3\ln \frac { x } { \sqrt [ 3 ] { z } }ln3z​x​

Use the Properties of Logarithms to Write $\ln \frac { x } { \sqrt [ 3 ] { z } }$