Solve Exponential Equation: 5^(sqrt(x)) + (1/5)^(sqrt(x)) = 25

[scientifico]

Homework Statement

5^( \sqrt(x) ) + 5 * 5^(- \sqrt(x) ) = 25 + 1/5

2. The attempt at a solution

I have thought to transform 5^ (-\sqrt(x) ) in (1/5)^(\sqrt(x) ) but I don't know how to solve then... could you help me ?

thank you

 

[Dick]

Homework Statement

5^( \sqrt(x) ) + 5 * 5^(- \sqrt(x) ) = 25 + 1/5

2. The attempt at a solution

I have thought to transform 5^ (-\sqrt(x) ) in (1/5)^(\sqrt(x) ) but I don't know how to solve then... could you help me ?

thank you

That's a good idea. So if u=5^(sqrt(x)) then 5^(-sqrt(x)) equals 1/u. Solve for u first.