# 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 31 ^{st} root of a 35 digit number?**

This can be answered even without knowing the number.

Log of 35^{th} digit number is 34. …

Log of 31^{st} 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, 31^{st} root of a 35 digit number is 13.

**3. What is the 64 ^{th} 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.**

This was really helpful! Thanks!

Being a bio student, it was difficult for me to find logarithms of different set of numbers. Thanks A lot!

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

sdfa

interesting one…keep it up…