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.
