Curriculum
General Mathematics — Second Secondary
Unit 1: Real Functions and Curve Sketching
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Unit 2: Exponents, Logarithms and Applications
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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 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
Properties of Logarithms
Properties of Logarithms
The basic laws
The basic laws
- If a > 0
- a ≠ 1
- and x > 0 and y > 0
- then:
| Law | Formula |
|---|---|
| Logarithm of a product | loga (xy) = loga x + loga y |
| Logarithm of a quotient | loga (x / y) = loga x − loga y |
| Logarithm of a power | loga (xn) = n loga x |
| Logarithm of the base | loga a = 1, and loga 1 = 0 |
- These laws turn products into sums, quotients into differences, and powers into multiples.
- This is why logarithms were once used to simplify long calculations.
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