Chapter 4.5, Problem 29E

Solution

To expand: The given logarithmic expression.

  $\frac{3}{4}\ln x$

Given:

An expression $\ln \sqrt[4]{x^3}$.

Concept used:

If $m$ and $n$ are positive numbers then $\ln m^n=n\ln m$ . This rule is known as the power rule.

Calculation:

  $\ln \sqrt[4]{x^3}=\ln x^{\frac{3}{4}}$

Apply the power rule.

  $\frac{3}{4}\ln x$

Conclusion:

The expansion of $\ln \sqrt[4]{x^3}$ is $\frac{3}{4}\ln x$.