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Topic 2: Logarithms and logarithmic functions

Logarithms and logarithmic laws

5 hours

• Define logarithms as indices, where 𝑎𝑥 = 𝑏 is equivalent to 𝑥 = log𝑎(𝑏), and convert between both forms. 1 interactive
• Use logarithmic laws and definitions  log𝑎(𝑥) + log𝑎(𝑦) = log𝑎(𝑥𝑦)  log𝑎(𝑥) − log𝑎(𝑦) = log𝑎 (𝑥 𝑦)  log𝑎(𝑥𝑛) = 𝑛log𝑎(𝑥)  log𝑎(𝑥) = log𝑏(𝑥) log𝑏(𝑎)  log𝑎(𝑎) = 1  log𝑎(1) = 0
• Solve equations involving indices using logarithms, with and without technology.

Logarithmic functions

7 hours

• Recognise and determine the qualitative features of the graph of 𝑦 = log𝑎(𝑥) (where 𝑎 > 1), including asymptote and intercept. 1 interactive
• Recognise and determine the effect of the parameters 𝑎, ℎ and 𝑘 on the graph of 𝑦 = log𝑎(𝑥 − ℎ)+ 𝑘 (where 𝑎 > 1), with and without technology.
• Sketch graphs of logarithmic functions, with and without technology.
• Solve equations involving logarithmic functions with and without technology.
• Model and solve problems that involve logarithmic functions, e.g. decibels in acoustics and the Richter scale for earthquake magnitude, with and without technology.