Indices and Logarithms - I — O/L Mathematics

What must I remember about Indices and Logarithms - I?

• Multiplication and division index laws: aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ / aⁿ = aᵐ⁻ⁿ.
• Power of a power and distribution laws: (aᵐ)ⁿ = aᵐⁿ; (ab)ⁿ = aⁿbⁿ; (a / b)ⁿ = aⁿ / bⁿ.
• Zero and negative index definitions: a⁰ = 1 (a ≠ 0); a⁻ⁿ = 1 / aⁿ.
• Fractional index definition: a^1/n = ⁿ√a; a^m/n = ⁿ√(aᵐ) = (ⁿ√a)ᵐ.
• Solving exponential equations: Express both sides with the same prime base and equate exponents (if aˣ = aʸ, then x = y for a > 0, a ≠ 1).

Test yourself (1 minute)

1. Common base reduction

   In equations like 4^x+1 = 8^x-1, convert both bases to 2: (2²)^x+1 = (2³)^x-1 ⟹ 2x + 2 = 3x - 3 ⟹ x = 5.

2. Negative fractional exponent handling

   16^-3/4 = 1 / 16^3/4 = 1 / (⁴√16)³ = 1 / 2³ = 1/8.

3. Addition of indices trap

   aᵐ + aⁿ NEVER equals aᵐ⁺ⁿ; index laws apply to MULTIPLICATION and DIVISION, never to addition or subtraction.

Practise Indices and Logarithms - I questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 2)

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Grade 11 · Term 1