Back to Course

SS1: MATHEMATICS - 1ST TERM

0% Complete
0/0 Steps
  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



  • Do you like this content?

  • Follow us

Lesson Progress
0% Complete

Logarithm of a number to a given base is the index to which the number must be raised to give the number.

Expressed mathematically;

\( \scriptsize b^x = a \: \leftrightharpoons \: \log_b a = x \)

Here are examples to help you understand the conversions from one form to the other form.

a. \( \scriptsize 3^2 = 9 \: \leftrightharpoons \: \log_3 9 = 2 \)

b. \( \scriptsize 4^3 = 81 \: \leftrightharpoons \: \log_4 81 = 3 \)

c. \( \scriptsize 8^y = 2 \: \leftrightharpoons \: \log_8 2 = y \)

Other examples:

Index
Form
Logarithmic
Form
\( \scriptsize 2^4 = 16 \)\(\scriptsize \log_2 16 = 4 \)
\( \scriptsize 6^2 = 36 \)\(\scriptsize \log_6 36 = 2 \)
\( \scriptsize 3^{-2} = \normalsize \frac{1}{9} \)\(\scriptsize \log_3 \normalsize \frac{1}{9} \scriptsize = -2 \)

Common Logarithms:

Common logarithm is simply, a log with base 10. Base 10 is used because it is the base of our decimal system of numbers. A common log means log10. But usually, writing “log” is sufficient instead of writing log10. i.e., log100 = log10100.

So when you see a log with no base it means that it is log10.

Examples:

a. \( \scriptsize 10^2 = 100 \: \leftrightharpoons \: \log_{10} 100 \: or \: \log 100 = 2 \)

a. \( \scriptsize 10^{-2} = 0.01 \: \leftrightharpoons \: \log_{10} 0.01\: or \: \log 0.01 = -2 \)

Responses

Your email address will not be published.

back-to-top
error: