Global North | A nice Olympiad Exponent | Solve for x in this Problem

[@jagadiswarchakraborty295]

Thanks

[@superacademy247]

Welcome

[@RyanLewis-Johnson-wq6xs]

8^8=2^(8+2(8)) 16777216=16777216 x=8 It’s in my head.

[@walterwen2975]

A nice Olympiad Exponent: xˣ = 2⁸⁺²ˣ; x =?
xˣ = 2⁸⁺²ˣ = (2⁸)(2²ˣ), 2²ˣ > 0; xˣ/(2²ˣ) = (x/2²)ˣ = (x/4)ˣ = 2⁸ = (8/4)⁸; x = 8
Answer check:
x = 8: 2⁸⁺²ˣ = 2⁸⁺²⁽⁸⁾ = 2²⁴ = 2³⁽⁸⁾ = (2³)⁸ = 8⁸ = xˣ
Final answer:
x = 8

[@anniesworldeverythingsurro8214]

X =8