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# LOGARITHMS

CONTENT:

1. Use Of Logarithm Table And Antilogarithm Table In Calculations Involving

• Multiplication
• Division
• Powers
• Roots

2. Application of logarithm in capital market and other real life problems

Logarithm and antilogarithm tables are used to perform some arithmetic basic operations namely: multiplication and division. Also, we use logarithm in calculations involving powers and roots.

The basic principles of calculation using logarithm depends strictly on the laws on indices. Recall that,

(a) $$Log MN = Log M + Log N$$

(b) $$Log \frac{M}{N} = Log M -Log N$$

Hence, we conclude that in logarithm;

1. When numbers are multiplied, we add their logarithms
2. When two numbers are dividing, we subtract their logarithms.

## Multiplication of Numbers using Logarithm Tables

Example 1: Evaluate 92.63 × 2.914

Solution

Number Standard Form Log Operation
92.63 9.263 x 101 1.9667
2.914 2.914 x 100 0.4645 add
2.4312

Antilog of 2.4312 = 269.9

Example 2: Evaluate 34.83 × 5.427

Solution

Number Standard Form Log Operation
34.83 3.483 × 101 1.542
5.427 5.427 × 100 0.7346 add
2.2766

Antilog of log 2.2766 = 189.1

Class Activity:

Evaluate the following:

1. 6.26 × 23.83
2. 409.1 × 3.932
3. 8.31 × 22.45 × 19.64
4. 431.2 × 21.35

## Division of Numbers Using Logarithm

Example 1: Evaluate 357.2 ÷ 87.23

Solution

Number Standard Form Log Operation
357.2 3.572 x 102 2.5529
87.23 8.723 x 101 1.9406 subtraction
0.6123

Antilog of 0.6123 = 4.096

Example 2: Use a logarithm table to evaluate 75.26 ÷ 2.581

Solution

Antilog of 1.4647 = 29.16

Class Activity:

Use table to evaluate the following:

(1) 53.81 ÷ 16.25 (2) 632.4 ÷ 34.25 (3) 63.75 ÷ 8.946 (4) 875.2 ÷ 35.81

## Powers Using Logarithm

Study these examples.

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