时间复杂度为 2^O(log(n))

Question

I'm working on a practice exam and came across this problem:

True or false: 2 ^O(log(n)) = O(n).

I'm not really sure how to figure this out.

I wanted to try to apply the definition for big-o, but I'm not sure how that works with it because of the power of two.

Answer 1

Therefore, (1) cannot be true.

Answer 2

Mathematically this is false, because e != 2 it should be e^O(logn) = O(n) , but i guess it depends on the context because in terms of time complexity of a function or program, this almost true. If the question specifies its base 2 log though, it is totally true.