Learning objectives
Sketch the graphs of y = aˣ, y = eˣ, y = log_a x and y = ln x, stating the domain, the range and the equation of the asymptote for each, and describe them as inverses of one another
Sketch transformed graphs of the form y = k e^(nx) + a and y = k ln(ax + b) for integer constants, identifying intercepts and asymptotes
Apply the laws of logarithms for products, quotients and powers, together with the change of base formula, to combine or split logarithmic expressions
Solve an equation of the form aˣ = b by taking logarithms of both sides, and solve equations that reduce to a quadratic in aˣ or in ln x
Solve logarithmic equations by combining terms into a single logarithm, converting to index form, and rejecting any root that would require the logarithm of a non-positive number
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