Easiest way to find the log of any number without tables
Well, it is often needed to get the logarithm of a number without log tables.
So, it is advisable to know a few common techniques which may be useful in finding the logarithm of many numbers (logarithm to the base 10).
Below I have mentioned some useful ways to find the logarithm of numbers :
1. log 2 = 0.3010
2. log 3 = 0.4771
3. log 7 = 0.8451
4. log e = 0.693
5. Learn the above 4 logarithms. They will be useful in computing the logarithm of other numbers that are frequently required in various competitive examinations
6. log (ab) = log a + log b -> first logarithm identity
7. log (a/b) = log a – log b -> second logarithm identity
8. log (a^b) = b loga -> third logarithm identity
9. now to compute the logarithm of many other numbers, we can use these identities along with the 4 standard algorithms mentioned above.
Let’s see some examples :
suppose you need to find log 5
now log 5 = log (10 / 2) = log 10 – log 2 (using second logarithm identity)
now we know that log 10 = 1
and log 2 = 0.3010
so log 5 = log 10 – log 2 = 1 – 0.3010 = 0.6990
this way, we were able to find log 5
now let us take more examples of computing log
suppose you are asked to find log 12
now log 12 = log (3 * 4) = log 3 + log 4 (using first logarithm identity)
now we directly know log 3 = 0.4771
but we need to calculate log 4
log 4 = log (2 * 2) = log 2 + log 2 (using first logarithm identity) = 2 log 2
alternatively, log 4 = log (2 ^ 2) = 2 log 2 (using third logarithm identity)
this way, log 12 = log 3 + 2 log 2 = 0.4771 + 2 * 0.3010 = 0.4771 + 0.6020 = 1.0791
find this using a calculator
you will conclude that our answer is correct up to 4 decimal places which is good enough for most competitive exams
using these small techniques, you can find the logarithm of a large number of numbers
however, there are a few limitations
logarithm of some numbers cannot be found using this method
for example, you cannot find log 11 using this technique
think why ?
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Hope this will help you in competitive exams