Couldn't help myself with GMP documentation.

Should've looked at

Wikipedia first, though this paragraph is still unclear (to me):

**Looking up**, as in "looking up in the tables"? Is this then what makes it efficient, the fact that computer has those tables already stored?

Without this stored table, this method isn't any more efficient, because

**antilogarithm ***is* exponentiation, right (or is there some subtle difference

(like between antiderivative and integral, I think ... ))?

*$\displaystyle cd = b^{\log_b c}*b^{\log_b d} = b^{\log_b c + \log_b d}$