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

Antilog of 2.4312 = 269.9

Example 2: Evaluate 34.83 × 5.427

Solution

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

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.