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?
581 words
O Focus
Page 4 of 4
+
100%
9:30 AM
2 Type here to search
4/24/2021](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb506c2a-87ff-481e-91d1-afe33e7e5fb4%2F41970358-1df0-43b2-971b-a9ad98aee131%2F1our2oz_processed.png&w=3840&q=75)
Transcribed Image Text:AutoSave O ff
Unit-4.Lesson-5.The-Method-of-Common-Bases - Protected View - Saved to this PC
Tierney Phillips (261335)
TP
File
Home
Insert
Design
Layout
References
Mailings
Review
View
Help
A Share
P Comments
1
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?
581 words
O Focus
Page 4 of 4
+
100%
9:30 AM
2 Type here to search
4/24/2021
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