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Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
3. Properties of Logarithms
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Exercise 1 Page 207

What formula tells you that a logarithm can be converted to any base that is a positive real number different than 1?

Change-of-Base

We want to complete the following sentence.

You can evaluate logarithms to any base using the ? formula.

Let's review the Properties of Logarithms that we know.
Name Formula
Change-of-Base Formula log_ax = log_bx/log_ba
Product Property log_a(uw) = log_au + log_av
Quotient Property log_au/v = log_au - log_av
Power Property log_au^n = nlog_au

In each formula, we evaluate a logarithm with base a, where a≠ 1 is a positive real number. Only in the first formula do we change the base for another positive real number different from 1. log_ax = log_bx/log_ba According to this formula, we can convert a logarithm to a different base. It is useful, for example, when we want to represent the expression using only natural logarithms. Since a natural logarithm is a logarithm with a base of e we can use the Change-of-Base formula. log_ax = lnx/lna In summary, the Change-of-Base formula is used to change the base of any logarithm. Let's complete the sentence.

You can evaluate logarithms to any base using the Change-of-Base formula.

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arrow_right Vocabulary and Concept Check p.207
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arrow_right Procedures and Problem Solving p.207-209
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arrow_right Conclusions p.209
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arrow_right Cumulative Mixed Review p.209
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