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5^(2x) - 26*5^x + 25 = 0
Introduce new variable u = .
Then the equation takes the form
u^2 - 26u + 25 = 0.
Factor left side
(u-25)*(u-1) = 0.
The roots of this equation are u= 25 and u= 1.
If u= 25, then = 25 = ; hence, x = 2.
If u= 1, then = 1 = ; hence, x = 0.
ANSWER. The original equation has two solutions: x= 0 and x= 2.
Solved.
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Introducing new variable is a standard method for solving such equations.
To see numerous examples of solving exponential equations, look into the lessons
- Solving exponential equations
- Solving advanced exponential equations
- OVERVIEW of lessons on solving exponential equations
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Exponential equations".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.