Lesson 3

To determine the magnitude of an earthquake, the logarithmic notation y = log x was used, where the base was 10. This allowed the use of a calculator to determine the answer using the logarithmic function. When the base is not 10, evaluating logarithmic notation is problematic, and, therefore, using the exponential notation becomes useful.

Try evaluating log2 32 on your calculator. Did you get 1.505 14…? If you did, then you entered log 32 (log10 32). When entered in this way, the calculator assumes that the base is 10. One method to evaluate log2 32 is to use its equivalent exponential notation, 32 = 2y, and solve for y as follows:

32 = 2y

25 = 2y

Because the base is the same on both sides of the equal sign, the exponents must be equal; therefore, y = 5.

View Evaluating Logarithms for more examples of how to evaluate logarithms.

Self-Check 2

Evaluate each of the following logarithmic expressions.

1.  Answer
2.  Answer
3. log2 (−8) Answer