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Exercises Exponentials and logarithms

Example 1 from Algebra and Trigonometry, 6.4 Graphs of Logarithmic Functions

Identifying the Domain of a Logarithmic Shift

What is the domain of $f (x) = \log_{2} (x + 3) ?$

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 logarithmic function is defined only when the input is positive, so this function is defined when $x + 3 > 0.$ Solving this inequality,

$\begin{array}{l} x + 3 > 0 & The input must be positive . \\ x > - 3 \begin{matrix} \end{matrix} & Subtract 3 . \end{array}$
The domain of $f (x) = \log_{2} (x + 3)$ is $(- 3, \infty) .$

Your turn

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

What is the domain of $f (x) = \log_{5} (x - 2) + 1 ?$

How did it go?

PreviousEvaluating a Natural Logarithm Using a Calculator Next Identifying the Domain of a Logarithmic Shift and Reflection

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 6.4, 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.