Quick calculations for extremely large numbers
A guest post by Nandeesh H.N. of Kolkata
Quick calculations with a few logarithms
If you can remember a few logarithms, you can do many calculations quite easily without the aid of calculators or computers.
Try to remember the logarithms of just seven numbers:
Log 2 = 0.30, log 3 = 0.48, log 7 = 0.85, log 11= 1.04, log 13= 1.11, log 17 = 1.23 and log 19=1.28.
The logarithm of a composite number is equal to the sum of the logarithms of its prime factors; you can formulate the following table of logarithms:
| Number | Logarithm | Number | Logarithm |
| 2 | 0.30 | 11 | 1.04 |
| 3 | 0.48 | 12 | 1.08 |
| 4 | 0.60 | 13 | 1.11 |
| 5 | 0.70 | 14 | 1.15 |
| 6 | 0.78 | 15 | 1.18 |
| 7 | 0.85 | 16 | 1.20 |
| 8 | 0.90 | 17 | 1.23 |
| 9 | 0.95 | 18 | 1.26 |
| 19 | 1.28 |
Note: Logarithm of 11 is 1.04. It means log 1.1 = 0.04. Log 5 = log (10/2) = log10 – log 2.
With the above figures in hand you can do a lot of calculations quite easily.
1. What is 2 raised to power 37?
Logarithm of 2 is 0.30.
37 times 0.30 is 11.10
Since logarithm of 1.2 is 0.08 and logarithm of 1.3 is 0.11, antilog of 0.10 is about 1.26.
So antilog of 11.10 is 1.26 * 10^11.
That is 2^37 = 1.26 * 10^11.
2. What is the 31st root of a 35 digit number?
This can be answered even without knowing the number.
Log of 35th digit number is 34. …
Log of 31st root = 34. …./ 31
This lies between 34/31 and 34.99/31 or between 1.09 and 1.13.
From the above table, we can see that in this interval, logarithm of 13 is 1.11.
So, 31st root of a 35 digit number is 13.
3. What is the 64th root of a 20 digit number? Answer is 2.
4. What is the cube root of say 74567?
Log of 74567 = 4.873 (interpolating between log 7 =0.85 and log 8 = 0.90).
4.873 / 3 = 1.624.
Antilog of 0.624 is 4.24 (because log 4 = 0.60 and log 5 = 0.70).
So, cube root of 74567 is about 42.4
This post is contributed by Nandeesh Nagarajaia. He is a Chemical Engineer who did his B.Tech from NIT Suratkal. He is now in IT field as Assistant General Manager(Systems) in Hindustan Copper Limited. He love Maths and enjoy teaching Maths to his sons.
On behalf of all the QuickerMaths.com users, I am highly grateful for his contribution.
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March 4th, 2013 - 16:59
Sir please help to find values of these kind of problems @^37 or 34^45 etc
March 4th, 2013 - 16:58
sir I didn’t understood how 2^37 came can you please help me how to find values in such cases
May 28th, 2012 - 14:06
hello vaneet sir,i’ve been preparing for the bank po exam but the quantitative aptitude the huge calculations are making it too tough for me to get through plz sir help us m sure a number of students wud b looking for some sort of shotcuts on these kind of problems
for example:- 39.23%of 653+ 47.39%of 433=approx_%of 553
plz sir help me wid these problems how to calculate this
thanx
March 5th, 2013 - 23:00
In such problems we need to do lot of approximation and use options as much as possible
For example, exact: 39.23%*653 = 256.17; approximation: 40%*650 = 260
exact: 47.39%*433 = 205.2; approximation 48%*430 = 50%*430 – 2.5%*430 = 215 – 11 (approx) = 204
Hence total of LHS = 464.
464/553 = 84% (approx). Now use the options.
November 11th, 2011 - 09:26
sdfa
August 24th, 2010 - 00:49
interesting one…keep it up…