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Exercises Exponentials and logarithms

Example 5 from Algebra and Trigonometry, 6.3 Logarithmic Functions

Finding the Value of a Common Logarithm Mentally

Evaluate $y = \log (1000)$ without using a calculator.

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
First we rewrite the logarithm in exponential form: $10^{y} = 1000.$ Next, we ask, “To what exponent must $10$ be raised in order to get 1000?” We know

$10^{3} = 1000$
Therefore, $\log (1000) = 3.$

Your turn

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

Evaluate $y = \log (1, 000, 000) .$

How did it go?

PreviousEvaluating the Logarithm of a Reciprocal Next Finding the Value of a Common Logarithm Using a Calculator

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 6.3, 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.