How do I calculate exponent (x^n) of a certain number (x) without self multiplication and without computers? Any efficient methods?

Question

I have a number 'x' raised to 'n', and I want to calculate the x^n without x.x.x.x....(n times). How do I do that? Is it possible to do it without the tedious self-multiplication?

(I mean to do it without computers)

I've been suggested using logarithms, but how efficient are they and do they have a limit?

Thanks