2^(x+2)-2^(x)=24

??

2^(x+2) - 2^x = 24

2^2 * 2^x - 2^x = 24

(2^x) (4-1) = 24

2^x = 8

well x = 3 works :)
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check :
2^5 - 2^3
32 -8
24
sure enough