# A description of the mean of the Geometric Distribution - is it unorthodox or just incorrect?

I have a homework assignment where I'm asked to propose an estimator for the mean of a geometric random variable. This seemed simple enough, given that I've always understood the mean of the geometric distribution to be $$1\over{p}$$. The directions, however, describe it this way:

Recall that the mean of a geometric random variable $$X$$ is given by $$\theta = \exp(\mathbb E[\log(X)])$$

I cannot understand this construal of the mean of a geometric distribution. I've tried manipulation with MGFs and it still doesn't make sense. Is there a typo in the homework directions or is this legitimately a way of describing the mean of X? If it's the latter, how does it work?

$$\exp(\mathbb E[\log(X)])$$
is the geometric mean of a positive random variable $$X$$