 # Find Log

Updated: 19 Aug 2023

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Logarithms are powerful mathematical tools with applications across various scientific, engineering, and mathematics. Whether solving complex equations, analyzing exponential form, or working with complicated calculations, understanding how to find log is crucial. To find log is difficult to find and solve, sol these rules are explained and simplified in the article “How to find log”.

## How to Find Log

It is difficult to find log of base-10 for learners and students.

## Common Logarithm

The common logarithm was invented by a British Mathematician, Prof. Henry Briggs (1560-1631).

### Definition of Common Logarithm

Logarithms having base 10 are called common logarithms or Briggs logarithms.
Note:
The base of the logarithm is not written because it is considered to be 10 .

### Parts of a common logarithm

The logarithm of the number consists of two parts.

#### Characteristics

The digit before the decimal point or Integral part is called the characteristics.

#### Mantissa

The decimal fraction part is the mantissa.

#### Example:

1.5377
In this example
Characteristics=1
Mantissa=.5377

## Log Table

The log table is organized into columns and provides a convenient way to find the logarithm of a given number.

### Parts of Log Table

A logarithm table is divided into three parts.

#### Main Column

The first part of the table, the main column, contains numbers from 10 \ to \ 99 .

#### Differences columns

The second part of the table, called differences columns, consists of 10 columns headed by 0, 1, 2, …. 9 .

#### Mean Differences

The third part consists of small columns known as mean differences headed by 1, 2, 3, … 9 .

### How to use a Log Table

• First, take the two digits of the number whose logarithm is required and see it in the row of the main column of the log table.
• Proceed horizontally along the selected row till the column headed by the third digit. The number under these columns is taken to find mantissa.
• Now see the fourth digit in the mean differences columns of the same row and add to the mantissa found in the second column.

## How To Find Mantissa

Here are the steps to find mantissa with example and explanation.

### Example to Find Mantissa

432.5
Solution:

• First, ignore the decimal point.
• Take the first two digits, e.g. 43 and proceed along this row until we come to the column headed by the third digit 2 of the number, which is 6355 .
• Now take the fourth digit, i.e. 5 and proceed along this row in the mean difference column, which is 5 .

## How to find the common logarithm

• Round off the given number to four significant figures.
• Find the characteristics of the logarithm.
• Find the Mantissa from the log table.
• Combine Characteristics and Mantissa.
##### Find logarithms of 2476

Solution:
2476
Let x=2476
Taking log on B.S
log \ ⁡ x=log \ ⁡2476
In Scientific form:
2.476 \times 10^3
Thus \ Characteristics =3
To find Mantissa, using Log Table
Mantissa =.3938 \quad \ As 3927+11
Hence log \ ⁡2476=3.3938

## Logarithm – MCQs

1. Logarithms having base 10 are called________ Logarithms
O Natural
O Common
O Briggs
O Both b & c

Common
Explanation:

2. Common logarithm is also called __________ logarithm
O Natural
O Briggs
O Both a & b
O None of these

Briggs
Explanation:

3. The digit before the decimal point or integral part is called _____________
O Characteristics
O Mantissa
O Both a & b
O None of these

Characteristics
Explanation:
In 1.5377 Characteristics is 1.

4. The decimal fraction part is called ________
O Characteristics
O Mantissa
O Both a & b
O None of these

Mantissa
Explanation:
In 1.5377 Mantissa \ is \ .5377 .

5. In 1.5377 , characteristics is
O 1
O .5377
O 1.5377
O None of these

1
Explanation:
The digit before the decimal point or Integral part is called characteristics.

6. In 1.5377 , Mantissa is
O 1
O .5377
O 1.5377
O None of these

.5377
Explanation:
The decimal fraction part is Mantissa.

7. The mean difference digits are added to ______________
O Characteristics
O Mantissa
O Both a & b
O None of these

Mantissa
Explanation:
The mean difference is the third part to find the mantissa and it is added to mantissa.

8 The mantissa of 763.5 is
O .8825
O .8828
O 2
O 76

.8828
Explanation:
(i). First ignore the decimal point
(ii). Take first two digits e.g. 76 and proceed along this row until we come to column headed by third digit 3 of the number which is 8825
(iii). Now take fourth digit i.e. 5 and proceed along this row in mean difference column which is 5.
Thus Mantissa of 763.5 \ is \ .8828

9. The characteristics of 982.5 is
O 0
O 2
O 3
O 4

2
Explanation:
First convert 982.5 to Scientific form:
9.825 \times 10^2
Thus Characteristics is 2

10. The characteristics of 7824 is
O 0
O 1
O 2
O 3

3
Explanation:
First convert 7824 to Scientific form:
7.824 \times 10^3
Thus Characteristics is 3

11. The characteristics of 56.3 is
O 0
O 1
O 2
O 3

1
Explanation:
First convert 56.3 to Scientific form:
5.63 \times 10^1
Thus Characteristics is 1

12. The characteristics of 7.43 is
O 0
O 1
O 2
O 3

0
Explanation:
First convert 7.43 to Scientific form:
7.43 \times 10^0
Thus Characteristics is 0

13. The characteristics of 0.71 is
O 1
O -1
O 2
O -2

-1
Explanation:
First convert 0.71 to Scientific form:
7.1 \times 10^{-1}
Thus Characteristics is -1

14. The characteristics of 37300 is
O 0
O 2
O 3
O 4

4
Explanation:
First convert 37300 to Scientific form:
3.73 \times 10^4
Thus Characteristics is 4

15. The characteristics of 0.00159 is
O 1
O -1
O -3
O -2

Explanation:
First convert 0.00159 to Scientific form:
0.00159 \times 10^{-3}
Thus Characteristics is -3

16. The mantissa of 2476 is
O .3927
O .3938
O 3
O None of these

Explanation:
(i). First ignore the decimal point
(ii). Take first two digits e.g. 24 and proceed along this row until we come to column headed by third digit 7 of the number which is 3927
(iii). Now take fourth digit i.e. 6 and proceed along this row in mean difference column which is 11.
Thus Mantissa of 2476 \ is \ .3938

17. The log of 2.4 is
O 24
O 0.3802
O 2.3802
O None of these

0.3802
Explanation:
See Ex # 3.3
Q No. 3
Part No. (ii)

18. The log of 482.7 is
O .6836
O 2.6836
O 2.6830
O None of these

2.6836
Explanation:
See Ex # 3.3
Q No. 3
Part No. (iv)

19. The log of 0.783 is
O .8938
O \overline{1} .8938
O 1.8938
O None of these

\overline{1} .8938
Explanation:
See Ex # 3.3
Q No. 3
Part No. (v)

20. The log of 0.09566 is
O \overline{2} .9805
O \overline{2} .9808
O 2.9808
O None of these

\overline{2} .9808
Explanation:
See Ex # 3.3
Q No. 3
Part No. (vi)

21. The log of 700 is
O .8451
O 1.8451
O 2.8451
O None of these 