SOLUTION: 5^(2x+1) + 25 = 5^(x+3) + 5^x

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Question 1094771: 5^(2x+1) + 25 = 5^(x+3) + 5^x
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.
Your equation is

 = ,   or, which is the same,

 = 0.


Introduce new variable  u = .  Then your equation will take the form

 = 0.

Apply the quadratic formula to find the solutions for u:


 =  = .

 =  = 25;

 =  = .


From  = 25 =  you get the solution for x: x= 2.

From  =  =  you get another solution for x: x= -1.


Answer.  The original equation has two solutions:  x = 2  and  x = -1.

The method of introducing new variable I showed you in this solution, is the standard method for problems like this.


To see more examples of problems solved in this way, see the lesson
    - Solving exponential equations
in this site.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
5^(2x+1) + 25 = 5^(x+3) + 5^x




(a * a * 5) – (a * 125) – a + 25 = 0 -------- Substituting 

5a(a - 25) - 1(a - 25) = 0
(5a – 1)(a – 25) = 0
5a – 1 = 0	OR 		a – 25 = 0 
5a = 1		OR		a = 0 + 25 
		OR		a = 25

   	    OR 	      
	    OR	      
	    OR

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