Curriculum
Pure Mathematics — Second Secondary
Unit 1: Real Functions and Curve Sketching
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Unit 2: Exponents and Logarithms
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Rational Exponents
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Rational Exponents — Lesson quiz
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The Exponential Function and Its Applications
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The Exponential Function and Its Applications — Lesson quiz
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Solving Exponential Equations
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Solving Exponential Equations — Lesson quiz
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The Inverse Function
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The Inverse Function — Lesson quiz
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The Logarithmic Function
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The Logarithmic Function — Lesson quiz
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Properties of Logarithms
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Properties of Logarithms — Lesson quiz
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Unit 3: Limits
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Unit 4: Trigonometry
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Text lesson
The Logarithmic Function
The Logarithmic Function
Basic properties and the domain
Basic properties and the domain
- From the definition we obtain the following basic properties
- where a > 0 and a ≠ 1:
| Property | Reason |
|---|---|
| loga 1 = 0 | Because a0 = 1 |
| loga a = 1 | Because a1 = a |
| loga (an) = n | Because n is the exponent that gives an |
| aloga x = x | Because the logarithm and the power are inverse operations |
- The domain of a logarithmic function is ]0, ∞[, so the logarithm is not defined for zero or for negative numbers.
- Its range is the set of all real numbers.
The Logarithmic Function · 2 / 6