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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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The Antilog, or “Anti- Logarithm” of a number is the inverse technique of finding the logarithm of the same number. i.e., if log x = y then x = antilog (y)

log x = y ⇒ x = antilog (y)

For example:

  • log 1000 = 3, antilog (3) = 103 = 1000
  • log 100 = 2, antilog (2) = 102 = 100

When finding an antilogarithm, we use the anti-log table, look up the mantissa and then use the characteristic to fix the decimal point correctly to the answer.

Below is the antilog table for the common logarithm.

common anti log table 01 1638249085 e1661715572224
common anti log table 02 1638249130
common anti log table 03 1638249175
common anti log table 04 1638249199
common anti log table 05 1638249221

Example – How to Use the Antilog Table?

Each of the following indicial systems is in the form y = 10x, use the antilogarithm table to find the decimal number y.

(a) 100.2318
(b) 101.2574
(c) 102.2296

Solution

(a) Let y = 100.2318

Step – 1: Express the index as the sum of characteristic and mantissa, i.e,

100.2318 = 100 + 100.2318

Step – 2: Concentrate only on mantissa in this step. Use the first two digits after the decimal point to be the row number, which is 23, run your finger along the row and stop under 1 (the third digit of mantissa)

This gives 1702.

Step – 3: In the same row, look for the mean difference corresponding to the 4thdigit of mantissa. Add this to the value from Step – 2. Running your finger along row 23 and stopping under difference 8 will give 3.

Add 3 to 1702 = 1705

anti log table 211

Step – 4: Put a decimal point right after the first digit (of the number from Step – 3) always.
Then it becomes 1.705

Step – 5: Multiply the number from Step – 4 by 10characteristic and the result itself is the antilog of the given number.

Therefore, \( \scriptsize y = 10^0 \: \times \: 10^{0.2318} \\ \scriptsize = 1 \: \times \: 1.705 \\ \scriptsize = 1.705\)

(b) \( \scriptsize 10^{1.2574} = 10^{1 \:+\: 0.2574} \\ \scriptsize = 10^1 \: \times \: 10^{0.2574} \\ \scriptsize = 10\: \times \: 1.809 \\ \scriptsize = 18.09\)

(c) \( \scriptsize 10^{2.2296} = 10^{2 \:+\: 0.2296} \\ \scriptsize = 10^2 \: \times \: 10^{0.2296} \\ \scriptsize = 100\: \times \: 1.696 \\ \scriptsize = 169.6\)

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