Note that they likely messed up slightly, it'll be more or less exponential in some base but possibly not 2. However big O notation does require you to get the

Note that they likely messed up slightly, it'll be more or less exponential in some base but possibly not 2. However big O notation does require you to get the base correct (or at least provide an upper bound), you can't ignore it like you can ignore a multiplicative or additive constant.