Table of Contents |
By the one-to-one property of exponential functions, an equation of the form can be solved by setting
EXAMPLE
Solve the equation
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This is the original equation. |
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Apply the one-to-one property. |
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Solve for x. |
Sometimes the bases are not equal, but it is possible for the exponential functions to be written so that they have the same base.
EXAMPLE
Solve the equation
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This is the original equation. |
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Rewrite ![]() |
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Apply the property ![]() |
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Use the one-to-one property. |
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Solve for x. |
There are even times when it is difficult to write one base as the power of the other, but both bases can be converted to the same base.
EXAMPLE
Solve the equation
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This is the original equation. |
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Rewrite ![]() ![]() |
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Apply the property ![]() |
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Simplify both exponents. |
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Apply the one-to-one property. |
![]() ![]() |
Solve for x. |
SOURCE: THIS WORK IS ADAPTED FROM PRECALCULUS BY JAY ABRAMSON. ACCESS FOR FREE AT OPENSTAX.ORG/BOOKS/PRECALCULUS/PAGES/1-INTRODUCTION-TO-FUNCTIONS