Could someone please help me to solve this equation using exact values.

Question

9^(2x)+4(9^x)=21
and also check for extraneous roots.
thank you

Answer 1

this is just a quadratic in 9^x. So, it factors out as

9^(2x) + 4(9^x) - 21 = 0
(9^x + 7)(9^x - 3) = 0

9^x cannot be -7, so you are left with

9^x = 3
x = 1/2

Answer 2

thank you for answering the question! but I am still not understanding it properly. If you don't mind solving it step by step so I understand how its done.
Thank you

Answer 3

let u = 9^x
then, 9^(2x) = (9^x)^2 = u^2

Thus all you have is

u^2+4u = 21
u^2+4u-21 = 0
(u+7)(u-3) = 0

so, u = -7 or u=3
But, u = 9^x ...