Question

2的2m+1次方-2的m+1次方等于64则m等于？

Answer 1

2^(2m+1) - 2^(m+1) = 64,
2 · 2^(2m) - 2 · 2^m = 64
2^(2m) - 2^m = 32
(2^m)^2 - 2^m - 32 = 0
2^m = (1±√129)/2
m = log<2>[(1+√129)/2] = log<2>(1+√129) - 1