Logarithmic and exponential functions

Exponential Functions and Their GraphsSign up

understand the function y = a^x and sketch its graph for a > 1 and 0 < a < 1 · understand the function y = e^x as the exponential function and recognise its special role in calculus

Logarithms: Laws, Exponential Equations and Linear FormSign up

understand and use the laws of logarithms: log(ab), log(a/b), log(a^n), change of base · be able to solve equations of the form a^x = b using logarithms, including problems modelled by exponential growth and decay · be able to use logarithms to linearise relationships of the form y = a x^n and y = a b^x, and interpret the gradient and intercept of the linearised graph

e^x and ln x as Inverse FunctionsSign up

understand the function y = e^(kx) and its derivative ky' = y, including modelling applications of exponential growth and decay · understand and use the natural logarithm function y = ln x as the inverse of y = e^x, including sketching its graph and noting its domain