Roughly, two functions have the same order of
magnitude if each one is bounded by a constant
times the other. More precisely, f(x) and
g(x) have the same order of magnitude if
f(x) = O(g(x)) and g(x) = O(f(x)). For example: x+7 and 34x
have the same order of magnitude;
as do x + log(x) and x;
but x^{7} and x^{9} do not.

If f and g are asymptotically equal, then they have the same order of magnitude. The converse is not true.