Calculate log 3 base 2 using Euler Method.

euler_method.py

import math
step = 0.1



########## calculate log(2)
'''
log(1.1) ~= log(1.0) + log'(1.05) * 0.1
log(1.2) ~= log(1.1) + log'(1.15) * 0.1
...
log(2.0) ~= log(1.9) + log'(1.95) * 0.1
'''
arg_prv = 1
val_prv = 0

while arg_prv < 2:
    arg_nxt = arg_prv + step
    arg_mid = (arg_prv + arg_nxt) / 2
    val_nxt = val_prv + step / arg_mid # log'(x) == 1/x

    arg_prv = arg_nxt
    val_prv = val_nxt

log2 = val_nxt

print('log 2      :', log2)                     # 0.6928353604099601
print('math.log(2):', math.log(2))              # 0.6931471805599453
print('defference :', abs(log2 - math.log(2)))  # 0.00031182014998520913
print('')



########## calculate log(3)
'''
log(2.1) ~= log(2.0) + log'(2.05) * 0.1
log(2.2) ~= log(2.1) + log'(2.15) * 0.1
...
log(3.0) ~= log(2.9) + log'(2.95) * 0.1
'''
while arg_prv < 3:
    arg_nxt = arg_prv + step
    arg_mid = (arg_prv + arg_nxt) / 2
    val_nxt = val_prv + step / arg_mid # log'(x) == 1/x

    arg_prv = arg_nxt
    val_prv = val_nxt

log3 = val_nxt

print('log 3      :', log3)                     # 1.098242634663974
print('math.log(3):', math.log(3))              # 1.0986122886681098
print('defference :', abs(log3 - math.log(3)))  # 0.00036965400413579985
print('')



########## calculate log 3 base 2
'''
log 3 base 2 == log(3) / log(2)
'''

log32 = log3 / log2

print('log 3 base 2 :', log32)                      # 1.585142297030176
print('math.log(3,2):', math.log(3, 2))             # 1.5849625007211563
print('defference   :', abs(log32 - math.log(3, 2)))# 0.00017979630901976407
print('')