Exponential and logarithmic functions

Sections

1. 9A Indices Powers, the index laws for products, quotients and powers, and the meaning of zero and negative indices.
2. 9B Fractional indices The meaning of a^(1/n) and a^(m/n) as roots, converting between surds and indices, and why the base must be positive.
3. 9C Logarithms The definition of a logarithm, finding logs by writing numbers as powers, logs of fractions and roots, the calculator, and locating a log between two integers.
4. 9D The laws for logarithms Logs and exponentials as inverse functions, the three log laws, and the particular values log_a 1, log_a a and log_a (1/x).
5. 9E Equations involving logarithms and indices The change-of-base formula, solving index equations by matching bases or taking logs, equations that reduce to quadratics, log equations, and exponential inequations.
6. 9F Exponential and logarithmic graphs The graphs of y = a^x and y = log_a x, their asymptotes and key points, and how reflections, translations and dilations change them.
7. 9G Applications of exponential and log functions Exponential growth and decay models, doubling time and half-life, rearranging formulas between index and log form, and log scales such as pH.