Question

Find x if 2^2x-2^(x+3)+2⁴=0.

Answer 1

2^2x - 2^2 × 2^3 +16 = 0
Put t =2^x
t^2- 8t + 16=0
(t-4)(t-4)=0
2^x=2^2
x=2

Answer 2

2^2x can be written as (2^x)²

2^(x+3)=(2^x)(2³)

now substitute these values in the question ,we get

2^x(2^x-2³)=-2⁴

2^x(2^x-8)=-16

let 2^x be y

y(y-8)=-16

y²-8y+16=0

(y-4)²=0

y=4

but y =2^x

so 2^x=4=2²

x=2


I hope this will help u ;)