Question

2$2 ^{x-2}=8$

Answer 1

2^x-2 = 8
2^x-2 = 2^3

x-2=3

x=5

Answer 2

$2^{x-2}=8\\ \\ 2^{x-2}=2^3\\ \\ x-2=3\\ \\ \boxed{x=5}$