Questions on Logarithmic Functions

What's On This Page

This page contains sample problems on logarithmic functions. They are for Self-assessment and Review.

Each problem (or group of problems) has an "answer button" ANSWER which you can click to look at an answer. Some solutions have a "further explanation button" Explain which you can click to see a more complete, detailed solution.

What to Do

To gain the most benefit from these problems,

Work the problems on your own. Write down your solutions BEFORE looking at any answers.

Use a graphing calculator as appropriate. A graphing calculator can be used to verify that your answers "make sense" or "look right".

If you have difficulties with this material, please contact your instructor. (See Getting Help in Stage 1.) You realistically have a few Stages in which to catch up on logarithmic functions, but you will be learning new material at the same time. We do not offer a further review of logarithmic and exponential functions.

Evaluate the following. These should be done without a calculator.

  1. log381

  2. log51/125

  3. log 10,000

  4. ln (1/e3)


Give the domains of the following logarithmic functions:

  1. f(z) = ln z

  2. f(x) = log (x - 3)

  3. g(t) = log5(-t)

  4. h(x) = 1 - ln (x + 5)


You can find examples of the use of logarithms in solving exponential equations in the Questions on Exponential Functions found in this Field Guide.

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