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How can you make logarithm table is there any formula to make it?
Remyhina
The answer is rather complicated but I will do my best. Let's consider logs in base 2 as those are the easiest. We can make a table quite easily:
log2_1 = 0
log2_2 = 1
log2_4 = 2
log2_8 = 3, etc.
Notice that in order to get a whole number answer we had go by powers of 2. So we know the logarithms for 2, 4, 8 etc. But what if we want to find the logarithm of say 3? Now I don't quite remember where I saw this but to find a logarithm between two others we take:
logB_square root[X * Y] and [C + D] / 2 with the logs being logB_X = C & logB_Y = D with the log being between them. For example take:
log2_2 = 1 and log2_8 = 3 using the formula we get log2_sqrt[2 * 8] = [1 + 3] / 2 =
log2_4 = 2 which you can clearly see is between the two logs. Now to find log2 = 3 we take:
log2_2 = 1
log2_4 = 2
sqrt of 2 * 4 = 2.828 approximately and [1 + 2] / 2 = 0.5 so we get:
log2_2.828 = 0.5; to get closer that 3 is between log2_2.828 and log2_4 so using the formula on them we have: sqrt [2.828 * 4] and [0.5 + 2] = 1.25
log2_3.63 = 1.25; then continuing a few times:
log2_3.20 = 0.875; used log2_3.63 and log2_2.828
log2_3.00 = 0.6875; used log2_3.20 and log2_2.828
We can keep going getting closer and closer to 3. We got 3.00 because I was rounding the answers on the calculator. We can actually go on forever always getting closer. We stop when we notice we start getting the same answer. Notice that each time we used the formula we kept the log we wanted in between the 2 logs we used. This is IMPORTANT! If the log you want isn't in between the logs you use for the formula you will not get the right answer. Now this nowhere near precise but I hope you get the idea. To get more accuracy you should keep more decimal places. Like if you want 5 decimal places keep 6 and then when you're done round your answer. Also note that there is formula to change the base. It is:
[logB_C] / [logB_D] = logD_C
So once you make a table of logarithms in one base you can use the formula to conver them to any base you wish. I can always help clarify if anyone has trouble getting this.
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∙ 12y ago
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