Support · Mathematics Advanced 11–12 – Year 11 · Exponential and logarithmic functions
Support Derive the laws of logarithms from the laws of indices log_am + log_an = log_a(mn), log_am - log_an = log_a(m/n) and log_a(mⁿ) = nlog_am
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
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Prerequisite dot points
Use graphing applications to compare and contrast graphs for the functions y = a^x and y = log_ax
Stage 5 · Logarithms (Path) Draft mapping
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Generalise that y = log_ax is an increasing function when a > 1 and decreasing when 0
Stage 5 · Logarithms (Path) Draft mapping
No checked resources on this prerequisite dot point yet.
Recognise equivalence where y = a^x is equivalent to x = log_ay where a > 0and a≠1
Stage 5 · Logarithms (Path) Draft mapping
No checked resources on this prerequisite dot point yet.