8 Course 8 of 10
Exponentials and logarithms
When something grows or shrinks by a fixed percent, time ends up in the exponent: savings, populations, radioactive decay. This course covers exponential functions and their inverses, logarithms, and how to use both to answer real questions. Every lesson has examples worked step by step, practice problems with solutions and a quick check at the end.
Before you start: Algebra 2, especially rational exponents and inequalities.
Unit 1 Exponential functions
- 1 Exponential functions Exponential functions of the form f(x) = ab^x, growth versus decay, their graphs, asymptotes and transformations, and the natural base e. 12 min
- 2 Solving exponential equations with a common base Solving exponential equations by rewriting both sides with the same base, equations with no solution, and equations that are quadratic in form. 11 min
- 3 Exponential inequalities Solving exponential inequalities by comparing exponents, keeping or reversing the inequality depending on the base, including quadratic-in-form inequalities. 10 min
Unit 2 Logarithms
- 4 Logarithms The definition of a logarithm, converting between logarithmic and exponential form, evaluating logarithms, common and natural logs, and domain restrictions. 11 min
- 5 Properties of logarithms The product, quotient and power rules, expanding and condensing logarithmic expressions, the change-of-base formula and logarithmic scales like pH. 12 min
- 6 Logarithmic functions and their graphs The logarithmic function as the inverse of an exponential function, its graph, domain, range and vertical asymptote, transformations and finding domains. 11 min
Unit 3 Equations, inequalities and models
- 7 Solving logarithmic and exponential equations Solving logarithmic equations by converting to exponential form or using properties, checking for extraneous solutions, and solving any exponential equation with logarithms. 13 min
- 8 Logarithmic inequalities Solving logarithmic inequalities by combining the domain with an inequality between the arguments, keeping or reversing the sign depending on the base. 10 min
- 9 Exponential growth and decay models Compound interest, continuous compounding, population growth, depreciation, half-life, and using logarithms to find how long something takes. 13 min