[Southack]

100₁₀ is an order of magnitude larger than 10₁₀, but 100₂ is .3 orders of magnitude larger than 10₂, because 4/2 = 2, and log₁₀2 is about 0.30103.

And what is Log₂ 2?

[jejones]

One, by definition, because x¹ = x for any x, but what difference does that make?

[captain11]

100₁₀ is an order of magnitude larger than 10₁₀, but 100₂ is .3 orders of magnitude larger than 10₂, because 4/2 = 2, and log₁₀2 is about 0.30103.

True, though more generally you can express order of magnitude in bases othan 10. In the general case, a given number expressed in base n is made an order of magnitude larger (in that base) by shifting left one position (e.g. this applies whether talking about 100₂ and 10₂, or 100₁₀ and 10₁₀.