from __future__ import division
import math

def logN(X, base = math.e, decimalplaces = 12):
    integer_value=0
    while X < 1:
        integer_value -= 1
        X *= base
    while X >= base:
        integer_value += 1
        X /= base
    result = str(integer_value) + '.'
    X **= 10                         # Calc X to the 10th power
    while decimalplaces > 0:
        digit = 0
        while X >= base:
            digit += 1
            X /= base
        result += str(digit)
        X **= 10                       # Calc X to the 10th power
        decimalplaces -= 1
    return result


if __name__ == '__main__':
    value = 4.5
    print "                        X  =", value
    print " 3 decimal places   LOG(X) =", logN(value, base = 10, decimalplaces = 3)
    print " 6 decimal places   LOG(X) =", logN(value, base = 10, decimalplaces = 6)
    print "12 decimal places   LOG(X) =", logN(value, base = 10, decimalplaces = 10)