How can I use simple mathematical formulas to get to the natural log of a number (I can only use (^,*,/,+,-))?

You could carry out a Taylor series expansion around "e", since ln(e)= 1. You need calculus to derive the Taylor expansion for your initial algorithm, but it is all numbers after that.

See http://mathworld.wolfram.com/TaylorSeries.html for how Taylor series expansions work, and they even have an expansion for ln(x) in the examples!

Not possible to my knowledge. The difficulty is as follows. To get a natural logarithm you to have have 10 raised to the power of some number to equal your number.This is not possible with normal operations you suggest,

I don't remember the exact algorithm, but you can

find one in Volume 1, Chapter 1 of Knuth's book,

the art of computer programming. Look in the

section on logarithms.

Re: Avinash K's series: It only converges for

|x| <1 and for x =1 it converges to ln 2 very

slowly. It won't work for larger values of x.

ln(1+x)=x-(x^2)/2+(x^3)/3- and so on.using this formula,we can find the logarithms(at natural log) of any number greater than zero.For numbers less than zero,logarithms are not defined.