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Tables of Logarithms is taught in the note for Logarithms. Read it below and look for the section on this topic.

Logarithms

10 min read

Standard form

Standard form writes very large or very small numbers as where . For example and .

Worked exampleStandard form

Write 6 300 000 in standard form.

  1. Place the decimal point after the first digit: 6.3.
  2. Count how many places the point moved: 6.

Answer:

What is a logarithm?

Logarithm
The logarithm of a number is the power you must raise a base to in order to get that number. If then .
Powers and logarithms are opposites. We write log N for base 10.
Exponential and logarithm graphsThe graphs of y equals 2 to the power x and its inverse y equals the logarithm of x to base 2. Each is the mirror image of the other in the line y equals x. The exponential graph passes through (0, 1) and the logarithm graph through (1, 0).xyy = xy = 2ˣy = log₂ x(0, 1)(1, 0)
Try itLogarithm explorer

Slide and read . Doubling the number adds the same amount each time: that is why logs turn multiplying into adding.

Laws of logarithms

LawRule
Productlog(AB) = log A + log B
Quotientlog(A ÷ B) = log A − log B
Powerlog(Aⁿ) = n log A
Special valueslog 1 = 0 and log 10 = 1
Worked exampleUsing the laws

Simplify .

  1. Add logs to multiply.
  2. 1 000 is 10³.

Answer: 3

Check yourself What is log 1000?
Check yourself Write 0.0045 in standard form.

Key terms

Standard form
A × 10ⁿ with 1 ≤ A < 10.
Logarithm
The power to which a base is raised to give a number.
Antilogarithm
The number whose logarithm is given.

Summary

  • Standard form: A × 10ⁿ with A between 1 and 10.
  • log N = x means 10ˣ = N.
  • log(AB) = log A + log B; log(A/B) = log A − log B; log(Aⁿ) = n log A.
Laws of Logarithms