Change of Base

The following formulas can be used to find when your calculator has either an ln key or a log key.

or

Example 1

Find the value of .

Solution .

Since two to the fourth is 16 and two to the fifth is 32, we know that the result should be between 4 and 5 with the result closer to 4 than to 5. We will use both formulas to confirm that it does not make any difference which one we use.

= = 4.169925001

= = = 4.169925001

In the section on solving exponential and logarithmic equations we will go over how the change of base formulas are derived.

Example 2

Graph (in blue) and (in red) on the same coordinate system.

Solution .

Note in order to graph using your calculator you must enter either or