1. The problem statement, all variables and given/known data So in my biology class, my professor wants us to use the Nernst equation without using calculators. I personally think this is stupid. However, I have no choice, so today, I tried coming up with approximations of the log function. 2. Relevant equations We start with loga(b) = n, and we want to find n. 3. The attempt at a solution Method 1: b = an b = (1+(a-1))n b ~ 1+n(a-1) n ~ (b-1)/(a-1) The problem with this approximation is that it's only good when a~b. I suppose I could decompose the log function using the rule log(ab) = log(a) + log(b), but this is somewhat tedious. Method 2: f(x) = 1 + xf'(x0)/1! + x2f''(x0)/2! + ... Let a=e and b=1+x. loge(1+x) = x - x2/2 + x3/3 - x4/4 + ... xn/n This one is pretty bad. It's even worse than method 1, and the more terms I use, the worse it gets. I'm not sure what's going wrong here, but I think it's because xn grows much faster than n. Therefore, this approximation is only good for values close to 1, which is useless, since loge(1) = 0. Furthermore, changing the base to loga(1+x) form, I'd have to divide by loga(e), which is another problem. ------ Any help will be much appreciated.