2*5^(2x)-5^(x)-1=0

Answer 1

let y = 5^x
then
2 y^2 - y - 1 = 0
(2y+1)(y-1) = 0
y = -1/2 or y = 1

if 5^x = 1
x = 0

if 5^x = -1/2
ln (5^x) = ln (-1/2)
undefined, you may not take log of a negative number