Curriculum
Course: Pure Mathematics — Second Secondary
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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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Unit 3: Limits

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Unit 4: Trigonometry

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Text lesson

Solving Exponential Equations

Pure Mathematics — Second Secondary

Solving Exponential Equations

The equal-powers property

The equal-powers property

  • If a > 0 and a ≠ 1, then ax = ay if and only if x = y.
  • So the key step in solving an exponential equation is to write both sides with the same base, equate the exponents, and then solve the resulting linear or quadratic equation.
  • To write numbers with the same base we use prime factorisation. For example:
Number As a power of 2 As a power of 3
8 23 Not possible
9 Not possible 32
27 Not possible 33
16 24 Not possible
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