**Problem Statement:** *Given an integer n and base B, the task is to find the length of n! in base B.*

**Sample Problem Link:** http://lightoj.com/volume_showproblem.php?problem=1045

*In this problem set you can use Kamnestsky's Algorithm*

**Approach:**

In order to solve the problem we use Kamenetsky’s formula which approximates the number of digits in a factorial:

*f(x) = log10( ((n/e)^n) * sqrt(2*pi*n))*

The number of digits in n to the base b is given by-

**logb(n) = log10(n) / log10(b)**

Hence, by using properties of logarithms, the number of digits of factorial in base b can be obtained by -

**f(x) = ( n* log10(( n/ e)) + log10(2*pi*n)/2 ) / log10(b)**

This approach can deal with large inputs that can be accommodated in a 32-bit integer and even beyond that!

**Solve Link:** https://github.com/Remonhasan/algorithm/blob/master/Kamenetsky%20-Algorithm.cpp

## Discussion