Can You SOLVE This Nice Germany Math Olympiad Problem?

[@sarvagyakesarwani3998]

I solved it in a simpler way!
4^x + 4^x = 64
2^2x + 2^2x = 2^6 (Since 2^6 = 64)
2(2^2x) = 2^6
2^(2x+1) = 2^6
Since bases are equal, therefore powers are also equal.
2x+1 = 6
2x = 5
x = 5/2 = 2.5
Checking,
4^x + 4^x = 64
4^(5/2) + 4^(5/2) = 64
2^5 + 2^5 = 64
32 + 32 = 64 (Since 2^5 = 32)
64 = 64
LHS = RHS

[@Learnmathtrick]

Great method. Thank you