# How To Use Logarithm Table And Download Four Figure Table Pdf

A logarithm table is used to find the log and antilog of numbers. This is very useful when finding the multiplication and division of numbers. Before I put you through how to use it, you need to know how to convert numbers to standard form.

Kindly note that the link to download the figure table, which has both the logarithm and antilogarithm table has been provided below.

**Logarithm**

The logarithm of a number is in two parts, the characteristics and the mantissa. For example, 2.5735 has (2) as the characteristics(integer) and (.5735) as the mantissa.

If a number is in standard form, it is easy to see what the characteristics of its logarithm are.

(1) For example, log 734 has the characteristics of 2 i.e.

734 = 7.34 x 10^{2} in standard form

It is also worth noting that when using logarithms to perform calculations, we assume that the base is 10.

Let me now show you how to make use of the logarithm table to find the log of numbers below

Log 76.7

Firstly express 76.7 in standard form and that will be 7.67 x 10^{1}

So, log 76.7 = 1.

Now the other value after the decimal point will be:

- Go to your logarithm table and check where 76 is
- After you have found 76, you will see numbers (0-9) at the top
- You will then look for the value of 76 under 7 and that will be 8848

So log 76.7 = 1.8848

To find the logarithms of numbers less than 1 we use negative powers of 10. This kind of number does have negative characteristics and a positive mantissa.

For example

(2) find log 0.005812 using table

The first thing is to express the number in standard form

0.005812 = 5.812 x 10^{-3}

So log 0.005812 = -3 or bar 3

Then look for where 58 is in the table, and check through the value under 1

So 58 under 1 is 7642, then the difference 2 is (1)

So 58 under 1 difference 2 is (7642 + 1 = 7643)

Therefore, log 0.005812 = -3 + 0.7643 = bar(3).7643

**Anitlog**

For example, use antilogarithm tables to find the number whose logarithm is 4.8625

Solution

Let the number be n

Log n = 4.8625

N = antilog of 4.8625

= 10^{4.8625}

= 10^{4} + 10^{0.8625}

= 10000 x (this will be .86 under 2 difference 5) (7278 + 8 = 7286, this is then 7.278)

= 10000 x 7.278

= 72780

Therefore, the antilog of 4.8625 is 72780

**Using Log Table for Multiplication and Division**

To multiply and divide numbers, first express them as logarithms and then apply the addition and subtraction laws of indices to the logarithm. Steps to follow

Kindly note that multiplication will be addition while division will lead to subtraction

- Use the logarithm tables to change the numbers to logarithms
- Finally, use the anti-logarithm tables to change the logarithms back to numbers

Example, calculate (76.7 x 308.2) / 8.04

Solution

Number | log |

76.7 308.2 | 1.8848 +2.4889 |

4.3737 | |

8.04 | -0.9053 |

3.4684 | |

Next is to find antilog of 3.4684

Log n = 3.4684

N = antilog of 3.4684

= 10^{3.4684}

= 10^{3} + 10^{0.4684}

= 1000 x 2.941

= 2941

So, (76.7 x 308.2) / 8.04 = 2941

The values are given to 4 places of decimals, hence the term, four-figure tables. Each table consists of two pages, lying facing one another. On the leftmost column, you can see values of x being listed, in differences of .00 to 99 and in another case 10 to 99

On the row, x travels from 0 to 9, and the ‘differences’ side runs from 1 to 9 as well and this is the mean difference, which must be added to obtain the final value.

To download the figure table, click here