How calculator computes logarithm?

Hi everybody,

Here's I post my question. Is there a systematic way of finding logarithm of a number?

For exponential, we have the exponential series.

But for logarithm, we have the logarithmic series which is not very useful as the -1<x<=1 in ln(1+x).

Anyone?

Thanks in advance.;)

Is there a systematic way of finding logarithm of a number without using logarithm of another base?

erm since when to find a logorithm of a number do you need the logorithm of another base. I thought it was just

log5 (23) = x

so 5 ^ x = 25

x = 5

where do you need a log of another base. perhaps i am not understanding the question properly

log5 (25)=x

log5 (25)=[log10 (25)]/[log10 (5)]

x=2

Gandalf_Grey_, the example u show can be deduced by humans brains, ie 5^2=25 bcos they are such a nice numbers.

What if in the practical situation, it presents a funny number with decimals to be logarithm of? That's what I mean.:)

In those times without the advent of computers yet, they looked it up in tables?