The wikipedia article was actually pretty interesting on this point. They suggest that 10 is commonly used, but other bases may be contextually relevant.
> An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10
I guess you could think of it like a _really_ low precision float or something.
I suspect the phrase is a cliche often used to sound scientific and sometimes by folks unaware, like how description of growth as “exponential” is a cliche used by non-mathematical discussion.
I agree with this. As a layman, I've always understood "orders of magnitude larger" to just mean "way too big" and "exponential" growth to imply "out of control".
x^2 and 2^x manifestly both involve exponents, so I think it's valid - outside math class - to call anything involving accelerating growth "exponential".
> An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10
I guess you could think of it like a _really_ low precision float or something.
1: https://en.wikipedia.org/wiki/Order_of_magnitude