this exponential equation has different base,but same exponent.

Question

4^× -9(2^×)=-20
i know the 4 is just 2squared, but i am just a little confounded when taking it into practice ,plz help

Answer 1

4^x
= 2^(2x) = (2^x)^2

let y = 2^x , so your equation becomes
y^2 - 9y = -20
y^2 - 9y + 20 = 0
(y-4)(y-5) = 0
y = 4 or y = 5

then 2^x = 4 = 2^2
x = 2

or

2^x = 5
take log of both sides, and use log rules
x log2 = log5
x = log5/log2 = appr 2.322