(A Level) Logarithms and exponential functions

Learning objectives

Convert between index form and logarithm form, and use the laws of logarithms (change of base is not required) to combine, simplify and solve equations

Sketch y = eˣ, y = e^(kx) for positive and negative k and y = ln x, and use the fact that eˣ and ln x are inverse functions

Solve equations and inequalities with the unknown in an index, such as 3^(2x + 1) = 7 or 0.8ˣ < 0.05, by taking logarithms and reversing the inequality when dividing by a negative logarithm

Solve equations that are quadratic in eˣ or in aˣ, such as e^(2x) − 4eˣ + 3 = 0, and equations involving expressions such as ln(x + a)

Transform y = Axⁿ or y = A bˣ into a straight-line relationship between ln y and ln x (or x), and find the constants from the gradient and intercept of the graph