Which expression is equivalent to ln $\sqrt[5]{\frac{x}{10}} ?$
A) $\frac{1}{5} \ln x-\ln 2$
B) $\frac{\ln x}{5 \ln 10}$
C) $\frac{1}{5} \ln x-\frac{1}{5} \ln 10$
D) $\frac{\ln 5}{\ln x-\ln 10}$
E) $\frac{x}{10} \ln 5$

Question

Which expression is equivalent to  ln  $\sqrt[5]{\frac{x}{10}} ?$
A) $\frac{1}{5} \ln x-\ln 2$
B) $\frac{\ln x}{5 \ln 10}$
C) $\frac{1}{5} \ln x-\frac{1}{5} \ln 10$
D) $\frac{\ln 5}{\ln x-\ln 10}$
E) $\frac{x}{10} \ln 5$

Quizplus · Accepted Answer

Using properties of logarithms, $\ln \sqrt[5]{\frac{x}{10}}$ simplifies to $\frac{1}{5} \ln x - \frac{1}{5} \ln 10$, which matches choice C.

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