# Activities

• • • ##### Subject Area

• Math: Precalculus: Logarithmic Functions
• Math: College Algebra: Exponential and Logarithmic Functions

• ##### Author 9-12

40 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.0

• ##### Report an Issue

Change Of Base #### Activity Overview

Discover the change of base rule for logarithms by examining the ratio of two logarithmic functions with different bases.

#### Key Steps

• In Problem 1, students compare the graphs of two logarithmic functions with different bases. They are to use the Trace feature to determine the values of the bases.

Students then use a function table to determine the constant factor of the two functions.

• In Problem 2, students investigate the effect of the bases on the value of c by testing different values of the bases of logarithmic functions in the spreadsheet.

• Then students find a formula to calculate c algebraically by rewriting the general logarithmic function and using the properties of logs. They can then use the formula for c, to change the base of a logarithmic function.