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SS1: MATHEMATICS - 1ST TERM

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  1. Number Base System I | Week 1
    6 Topics
    |
    2 Quizzes
  2. Number Base System II | Week 2
    3 Topics
  3. Number Base System III | Week 3
    2 Topics
    |
    1 Quiz
  4. Modular Arithmetic I | Week 4
    2 Topics
  5. Modular Arithmetic II | Week 5
    2 Topics
  6. Modular Arithmetic III | Week 6
    3 Topics
    |
    1 Quiz
  7. Indices I | Week 7
    3 Topics
  8. Indices II | Week 8
    1 Topic
    |
    1 Quiz
  9. Logarithms I | Week 9
    3 Topics
  10. Logarithms II | Week 10
    4 Topics
    |
    1 Quiz



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Lesson 10, Topic 3
In Progress

Calculations using Logarithms

Lesson Progress
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The basic principles of calculation using logarithms depend on the laws of indices.

Example – Multiplication and Division:

Use tables to work out the following:

1. 26.52 × 9.184
2. 912.4  ÷ 94.35

Solution

1st Method

1. 26.52 × 9.184

Using the tables

i.e \( \scriptsize 10^{1.4235} \: \times \: 10^{0.9630} \)

= \( \scriptsize 10^{1.4235 \:+ \:0.9630} \rightarrow \left(x^a \: \times \: x^b = x^{a \: + \:b} \right) \)

= \( \scriptsize 10^{2.3865}\)

Using the anti-log \( \scriptsize \rightarrow 2.435 \)

Answer = 243.5

2nd Method

NoLog
26.52    1.4235
9.184+ 0.9630
    2.3865
Antliog of 0.3865
= 2.435
102 × 2.435
Ans = 243.5

2. \( \scriptsize 912.4\: \div \: 53.55 \)

Using the tables

1st Method

i.e \( \scriptsize 10^{2.9602} \: \div \: 10^{1.7288} \)

= \( \scriptsize 10^{2.9602 \:- \: 1.7288} \rightarrow \left(x^a \: \div \: x^b = x^{a \: – \: b} \right) \)

= \( \scriptsize 10^{1.2314} \) Using the anti-log \( \scriptsize \rightarrow 1.704\)

Answer = 17.04

2nd Method

NoLog
912.4    2.9602
53.551.7288
   1.2314
Antliog of 0.2314
= 1.704
101 x 1.704
Ans = 17.04

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