Indices and Logarithms I
Unit 2: Indices and Logarithms I — Complete Lesson Roadmap
Master zero, negative, and fractional indices, prime-base algebraic simplification, and exponential equations with step-by-step worked examples.
About This Unit
Indices and Logarithms I builds directly on Grade 10 index laws to introduce negative and fractional exponents. Questions from this unit appear regularly in Paper I (Part A) and form essential algebraic steps inside Paper II of the G.C.E. Ordinary Level examination. Follow the five structured lessons below in order for complete exam readiness.
Recap of Basic Index Laws & Zero Index
Review the product (\(a^m \times a^n = a^{m+n}\)), quotient, and power laws from Grade 10, and apply the zero index rule (\(a^0 = 1\)) to simplify monomials.
Start Lesson 1 →Negative Indices & Reciprocals
Convert negative exponents into positive index forms (\(a^{-n} = \frac{1}{a^n}\)) and evaluate numerical fractions raised to negative powers.
Start Lesson 2 →Fractional Indices
Connect fractional exponents to \(n^{\text{th}}\) roots (\(a^{\frac{m}{n}} = \sqrt[n]{a^m}\)) and evaluate general and negative fractional powers using prime factorization.
Start Lesson 3 →Simplifying Complex Algebraic Expressions
Combine positive, negative, and fractional indices in multi-step fractions by converting composite numbers (\(4, 8, 9, 27\)) to prime bases.
Start Lesson 4 →Solving Exponential (Indicial) Equations
Solve equations where the unknown is in the exponent (\(a^x = a^y \implies x = y\)) as well as power equations where the unknown is in the base.
Start Lesson 5 →