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To calculate log manually, the Taylor or Maclaurin series is generally used.
An accurate method to calculate the value of logarithms would be.
If we need to calculate the value log(25) as an example:
1) Divide 25 by the nearest power of 10. The condition must be 25 ≥ 10n.
2) The value of n is 1 because 25 ≥ 101. So the initial answer is 1.xxxxxx.
3) Divide 25 by 101. The result is 2.5.
4) Raise 2.5 by 10. So 2.510 ≈ 9536.7
(The number is raised to 10)
5) For the next values, the same process will be used.
6) Divide 9536.7 by the nearest power of 10.
7) 9536.7 ≥ 103 so n=3. The answer is now 1.3xxxxx.
8) 9536.7 / 103 = 9.5367
9) Raise 9.5367 to 10. 9.536710 = 6222733625
10) 6222733625 ≥ 10n so n=9. The answer is now 1.39xxxx.
11) Repeat the same process until you get the desired precision.
12) So log (25) ≈ 1.39794.
Generally, the Taylor or Maclaurin series is used to calculate log manually,
To learn more about logarithms refer here
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