5^2x+20*5^x-125=0

Answer 1

5^2x = (5^x)^2
So, make things easier to look at by letting

u = 5^x

Then you have

u^2+20u-125 = 0
(u+25)(u-5) = 0
u = -25 or 5

But, 5^x is never negative, so we end up with

u=5
5^x = 5
x = 1

check:

5^2 + 20*5 -125 = 25+100-125 = 0

Answer 2

5^a + 20*5^b = 0

a log 5 + log 20 + b log 5