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 :
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
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 upto 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
Kayson’s education is an online platform that helps and guides you in every step of your preparation. we provide candidates a very high-quality Study material, video lectures, doubt clearing sessions, online test series, mock tests for IIT JEE that is prepared by a group of trained and experienced professionals with IIT syllabus in mind.
Hope this will help you in competitive exams