Sunday, February 3, 2013

5^(2x)+20*5^x-125=0 Solve the equation.

We are asked to solve 5^(2x)+20*5^x-125=0 :
Rewrite as (5^x)^2+20*5^x-125=0 and let y=5^x to get
y^2+20y-125=0 and
(y+25)(y-5)=0 so y=-25 or y=5.
y cannot be -25 as 5^x>0 for all real x.
If y=5 then x=1. If x=1 then 25+20(5)-125=0.
x=1 is the solution.
The graph:

 

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