Solve the equation `5^(2x)+24.5^(x)-25=0`

Explanation

Let `5^(x)=t` then the given equation can reduce in the form
`t^(2)-24t-25=0`
`rarr(t-25)(t_1)=0impliest!=-1`
`:.t=25`
then `5^(x)=25=5^(2)` then `x=2`
Hence `x_(1)=2` is only one root of the original equation.