SOLUTION: solve 25^y+3(5^y)=4

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Question 1062567: solve 25^y+3(5^y)=4
Answer by ikleyn(52818) About Me  (Show Source):
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solve 25^y+3(5^y)=4
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Introduce new variable x = 5%5Ey.

Then your equation becomes 

x%5E2+%2B+3x+-+4 = 0.     ( <--- since 25 = 5%5E2 )

Factor this quadratic equation:

(x+4)*(x-1) = 0.

Its roots are x= -4 and x= 1.


Hence, we have two equations for y:


1.  5%5Ey = -4.   It HAS NO solutions.


2.  5%5Ey = 1.   It has the solution  y = 0.


Answer. The only solution to the original equation is y = 0.

It is the standard method of solving exponential equations.
See the lesson
    - Solving exponential equations
in this site.