how are logarithms programmed as a function in a calculator or other programmable devices

Question

anonymous · Answer

Generally it's done using a series

anonymous · Answer

The taylor series for example can get you the natural log of x (albeit a bit slowly):

$$ln(x) = \sum_{n=1}^\infty \frac{1}{n}(x-1)^n$$

anonymous · Answer

oh wow interesting concept

dumbcow · Answer

thats what i was thinking
there are more efficient programs they use which will give decent approximations

anonymous · Answer

Whoops, forgot the (-1)^{n+1}

anonymous · Answer

umm but what about square root functions do they just iterate throughtit

anonymous · Answer

until they find a match?

anonymous · Answer

$$ln(x) = \sum_{n=1}^\infty \frac{1}{n}(-1)^{n+1}(x-1)^n$$

anonymous · Answer

No, infinite series can get you good approximations for any function you like.

dumbcow · Answer

actually newtons method for finding zeroes can be used to approximate square roots

anonymous · Answer

thankyou polpak and dumbcow

dumbcow · Answer

your welcome,
actually i take that back i dunno if they would use newtons method in a program because it would have to be recursive

dumbcow · Answer

prob infinite series like with logs