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Exercises Exponentials and logarithms

Example 3 from Algebra and Trigonometry, 6.3 Logarithmic Functions

Solving Logarithms Mentally

Solve $y = \log_{4} (64)$ 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: $4^{y} = 64.$ Next, we ask, “To what exponent must 4 be raised in order to get 64?”

We know

$4^{3} = 64$

Therefore,

$\log {}_{4}{(64)} = 3$

Your turn

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

Solve $y = \log_{121} (11)$ without using a calculator.

How did it go?

PreviousConverting from Exponential Form to Logarithmic Form Next Evaluating the Logarithm of a Reciprocal

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.