6 The Method of Common Bases works because exponential functions are one-to-one, i.e. if the outputs are the same, then the inputs must also be the same. This is what allows us to say that if 2" = 2', then x must be equal to 3. But it doesn't always work out so easily. If x = 5°, can we say that x must be 5? Could it be anything else? Why does this not work out as easily as the exponential case? %3D
6 The Method of Common Bases works because exponential functions are one-to-one, i.e. if the outputs are the same, then the inputs must also be the same. This is what allows us to say that if 2" = 2', then x must be equal to 3. But it doesn't always work out so easily. If x = 5°, can we say that x must be 5? Could it be anything else? Why does this not work out as easily as the exponential case? %3D
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The Method of Common Bases works because exponential functions are one-to-one, i.e. if the outputs are the same, then the inputs must also be the same. This is what allows us to say that if 2^x=2^3, then x must be equal to 3. But it doesn't always work out so easily.
If x^2=55^2, can we say that x must be 5? Could it be anything else? Why does this not work out as easily as the exponential case?

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5. The exponential function y=
25
- 10 is shown graphed along with the horizontal line y =115. Their
intersection point is (a, 115). Use the Method of Common Bases to find the value of a. Show your work.
(a. 115)
y =115
-10
y =
25
REASONING
The Method of Common Bases works because exponential functions are one-to-one, i.e. if the outputs are
the same, then the inputs must also be the same. This is what allows us to say that if 2 = 2', then x must be
equal to 3. But it doesn't always work out so easily.
If x = 5', can we say that x must be 5? Could it be anything else? Why does this not work out as easily as
the exponential case?
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