A question on Reimann (ref Prime Obsession by John Derbyshire)

I'm reading Prime Obsession by John Derbyshire, on the Riemann
Hypothesis.
And I've reached a line that I don't think I understand


He writes "[Natural] Log x increases slower than any power of x"

Obviously
Log 1 , log 2, log 3 increases from 0 to just over 1
and 1^2, 2^2, 3^2 increases from 1 to 9
So it is true for x^2


but is it true for, for example x^(0.002) ?


Is that what he means?

Thanks
Tony
.

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