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Exercises Exponentials and logarithms

Example 7 from Algebra and Trigonometry, 6.5 Logarithmic Properties

Using the Power Rule for Logarithms to Simplify the Logarithm of a Radical Expression

Expand $\log (\sqrt{x}) .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
$\begin{array}{l} \log (\sqrt{x}) & = \log x^{(\frac{1}{2})} \\ = \frac{1}{2} \log x \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Expand $\ln (\sqrt[3]{x^{2}}) .$

How did it go?

PreviousExpanding Logarithms Using Product, Quotient, and Power Rules Next Expanding Complex Logarithmic Expressions

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 6.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.