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Exercises Exponentials and logarithms

Example 3 from Algebra and Trigonometry, 6.5 Logarithmic Properties

Expanding a Logarithm with Powers

Expand $\log_{2} x^{5} .$

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
The argument is already written as a power, so we identify the exponent, 5, and the base, $x,$ and rewrite the equivalent expression by multiplying the exponent times the logarithm of the base.
$\log_{2} (x^{5}) = 5 \log_{2} x$

Your turn

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

Expand $\ln x^{2} .$

How did it go?

PreviousUsing the Quotient Rule for Logarithms Next Rewriting an Expression as a Power before Using the Power Rule

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.