At the end of the unit, learners should be able to demonstrate the following:
Learners can:
· State the laws of indices.
· Simplify expressions involving integral indices.
· Simplify expressions involving negative indices.
· Convert fractional indices into radical form.
· Convert radicals into fractional-index form.
· Simplify expressions involving fractional indices.
· Solve exponential equations.
· Use appropriate algebraic methods to solve index equations.
· Check solutions by substitution.
Learners can:
· Define a logarithm.
· Convert logarithmic expressions into exponential form.
· Convert exponential expressions into logarithmic form.
· Evaluate simple logarithms.
· State and apply the laws of logarithms.
· Expand logarithmic expressions.
· Condense logarithmic expressions.
· Solve logarithmic equations.
· Solve exponential equations using logarithms.
· Use common logarithms and natural logarithms where required.
· Apply the change-of-base formula.
· Identify restrictions on logarithmic expressions.
Learners can:
· Select an appropriate law or method when solving an indices or logarithms problem.
· Combine several laws in a single problem.
· Present solutions logically and clearly.
· Verify answers.
· Apply logarithms to exponential growth and decay problems.
· Interpret numerical answers in the context of a problem.
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