Solve:

5(5^x+5^-x)=26

5(5^x + 5^-x) = 26

let 5^x  = y so 5^-x = 1/y

5(y + 1/y) = 26

5( (y2 + 1)/y ) = 26

Assume 5^x=y. Then 5^-x becomes 1/y. By simplyfying you will get a quadratic in variable y. Solve and find the value of y by using quadratic formula. After getting the value of y by using the law i.e., if bases are equal then powers should be eqauted. Finally you will get the value of x.

 

                 PLEASE APPROVE IF I AM CORRECT

Let 5^x = t

 

Therefore, 5(t + 1/t) = 26

=> 5(t^2 + 1) = 26t

=> 5t^2 – 26t + 5 = 0

=> (5t-1)(t-5) = 0

t = 1/5, 5

5^x = 1/5, 5

 

Therefore, 

x = -1, 1