**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;

- When numbers are multiplied, we add their logarithms
- 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 × 10^{1} |
1.542 | |

5.427 | 5.427 × 10^{0} |
0.7346 | add |

2.2766 |

Antilog of log 2.2766 = 189.1

**Class Activity:**

Evaluate the following:

- 6.26 × 23.83
- 409.1 × 3.932
- 8.31 × 22.45 × 19.64
- 431.2 × 21.35

**D****ivision of Numbers Using Logarithm**

**Example 1: **Evaluate 357.2 ÷ 87.23

**Solution**

Number | Standard Form | Log | Operation |
---|---|---|---|

357.2 | 3.572 x 10^{2} |
2.5529 | |

87.23 | 8.723 x 10^{1} |
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**

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