# same order of magnitude

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 34*x*
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.

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