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Exercises Exponentials and logarithms

Example 4 from Algebra and Trigonometry, 6.5 Logarithmic Properties

Rewriting an Expression as a Power before Using the Power Rule

Expand $\log_{3} (25)$ using the power rule for logs.

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
Expressing the argument as a power, we get $\log_{3} (25) = \log_{3} (5^{2}) .$

Next we identify the exponent, 2, and the base, 5, and rewrite the equivalent expression by multiplying the exponent times the logarithm of the base.

$\log_{3} (5^{2}) = 2 \log_{3} (5)$

Your turn

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

Expand $\ln (\frac{1}{x^{2}}) .$

How did it go?

PreviousExpanding a Logarithm with Powers Next Using the Power Rule in Reverse

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.