Getting Started with Algebra 2
Changing Bases
Name ____________________________
Class ____________________________
ID: 9842
In this activity, you will explore:

Change-of-base formula
Open the file Alg2Act2_ChangeBase_EN.tns on your
handheld and follow along with your teacher to work
through the activity. Use this document as a reference
and to record your answers.
Many calculators can only compute common logarithms (base 10) and natural
logarithms (base e). While these two logarithms are the ones most frequently
used, sometimes you might need to evaluate logarithms of other bases. To do
this, the change of base formula is used. To discover this formula, some
exploration is required.
Evaluate the following using your TI-Nspire handheld.
(Note: The templates for Exercises 1–3 have already been entered into the TI-Nspire handheld
and may be found on pages 1.2–1.4.)
1. log7 5
2.
log3 7
log12 5
3.
log10 5
log10 7
4.
log2 10
log5 10
5.
log 5
log 7
6. Which of the expressions in Exercises 1–5 share the same value?
What do these expressions have in common?
7. Based on your answer to Exercise 6, match
each expression in Column A with an equivalent
expression in Column B. Then confirm your
answers using your handheld.
Column A
a. log3 2
b.
8. Rewrite the expression loga x as the
quotient of two logarithms.
log5.2 7
log5.2 3
c. log2 3
d.
loge 2
loge 7
Column B
log3 3
e.
log3 2
f. log7 2
g.
log3 2
log3 3
h. log3 7
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©2008 Texas Instruments Incorporated
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Getting Started with Algebra 2
9. The expression used in Exercise 8 is called the change of base formula. Why would we
need to know the change of base formula? Give an example of when we would use the
change of base formula.
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10. Beginning with the Change of Base formula (the whole equality), prove that this relationship
holds true for all numbers. Show all work below. (Hint: start with log a x  m and convert to
exponential form.)
©2008 Texas Instruments Incorporated
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