# Homework Help: Logarithmic function as an integral

1. Nov 17, 2011

### JMR_2413

1. The problem statement, all variables and given/known data
I'm attempting to prove the rules for the logarithmic function using the Integral definition: Log(x)=[1,x]∫1/t dt. I think im alright with the product rule but I'm struggling with the quotient rule: i.e. Log(a/b)=Log(a)-Log(b). I believe that I'm having trouble breaking up the Integral correctly. Any help would be appreciated!

2. Relevant equations

3. The attempt at a solution

2. Nov 18, 2011

### fzero

If you can show the product rule, then the quotient rule will follow the same logic, with an appropriate assumption about which of a or a/b is larger. Alternatively, use substitution to show that $\log(1/b) = - \log b$ so that you can combine this with the product rule.

3. Nov 18, 2011