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Just want to know if is there a way to find remainder of a division using logarithms.

To clarify the subject:

if we calculate $\log_{10}{3125}$ it is like: $3.494850021$.

I know if I subtract $3$ from the result and do the $10^\text{result}$ I'll get $3125/1000 = 3.125 $

I need the fraction part ($0.125$ or preferably $125$) and need it to get it in logarithms values.

In fact how to get (m mod n) using $\log_{10}{m}$ and $\log_{10}{n} $ and power of 10?

Anindya Prithvi
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A. choofe
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    If $m = bn + r; 0 \le r < n$ then $\log_{10} m = \log_{10} (bn+r)=\log_{10} n + \log_{10}(b + \frac rn)$ but you never be able to separate $b$ from $\frac rn$ and you can't split a logarithm on addition.

    Could you be more specific what you are trying to do and why you think it'd be at all doable?

     – fleablood Aug 30 '20 at 18:15
  • What I actually want to do is to separate first k digits from right using logarithms. like in the example I need to extract 125 from 3125. I can extract from right but needed the left digits though. Honestly I don't know if it is doable or not just searching! – A. choofe Aug 30 '20 at 18:36
  • mistakenly typed: I need from right digits. can extract from left but need right ones – A. choofe Aug 30 '20 at 18:43
  • Everything is doable, if you make enough specifics. But there is no real way to express $\log (A+ B)$ in terms of $\log A$ and $\log B$. – fleablood Aug 30 '20 at 18:45
  • Actually, Gaussian logarithms can be used to express $\log(A+B)$ in terms of $\log A$ and $\log B$ using another special function. However, I don't think that is going to help you. – Somos Aug 30 '20 at 20:44

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