How to find log 19 without calculator or tables
Answers
Answer:
xt 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.
This also works on logs with bases other than 10, even with decimals. In solving loga(x), just replace 10n with an. Also in solving for n, simply just divide the number by the base repeatedly until you get a quotient nearest to 1. The number of times you divided is n. (ie. 250/10= 25 (1), 25/10=2.5 (2), so n=2)
This is a method I had formulated on my own so I'm not saying that this is 100% reliable. It would be better to check your answer with a calculator. But I've tried this many times without flaws. No log tables, no need to memorize, just pure math.