Question

Solve this equation:

5^2x+1 + 24(5^x) = 5

The answer has to be -1 but I can't understand how to get this answer. Can someone please explain? Thanks!

Answer 1

let z= 5^x then


5z^2 + 24z -5=0
using quadratic equation
z= -24 +- sqrt 24^2+100 /10

z= -24 +- 26 /10

z= 1/5; z= -5

5^x= 1/5 >>> x=-1
or5^x= -5 >>> no possible x

Answer 2

Thanks! But how did you substitute 5z^2 for 5^2x+1?

Answer 3

5^(2x+1)= 5^1 * 5^2x= 5*5^2x= 5z^2