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

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The equation 5^(sqrt(x)) + 5 * 5^(-sqrt(x)) = 25 + 1/5 can be simplified by substituting u = 5^(sqrt(x)), leading to 5^(-sqrt(x)) being expressed as 1/u. This transformation allows for easier manipulation of the equation. The next step involves solving for u, which simplifies the overall problem. The discussion emphasizes the importance of substitution in solving exponential equations effectively.
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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
 
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scientifico said:

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.
 

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