(adsbygoogle = window.adsbygoogle || []).push({}); 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 log_{a}(b) = n, and we want to find n.

3. The attempt at a solution

Method 1:

b = a^{n}

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'(x_{0})/1! + x^{2}f''(x_{0})/2! + ...

Let a=e and b=1+x.

log_{e}(1+x) = x - x^{2}/2 + x^{3}/3 - x^{4}/4 + ... x^{n}/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 x^{n}grows much faster than n. Therefore, this approximation is only good for values close to 1, which is useless, since log_{e}(1) = 0.

Furthermore, changing the base to log_{a}(1+x) form, I'd have to divide by log_{a}(e), which is another problem.

------

Any help will be much appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Good Approximation to the Log Function

**Physics Forums | Science Articles, Homework Help, Discussion**