Precalculus · Grades 10 to 12
Logarithms and exponentials
Evaluate logarithms and solve exponential equations.
The idea
A logarithm answers the question: to what power do I raise the base? The statement log_b(x) = y means b^y = x.
Exponential equations become easier when both sides are written as powers of the same base.
Worked examples
- How to Evaluate a Logarithm Evaluate log base 2 of 32. Three steps, the power question, how to match exponents, and the base-and-answer mix-up to avoid.
- How to Solve an Exponential Equation Solve 3^x = 81 by writing both sides as powers of 3. Three steps, the matching-base reason, and the log mistakes to avoid.
- How to Solve a Logarithmic Equation Solve log base 2 of x = 5 by rewriting the log as a power. Three steps, the definition of a logarithm, and the domain mistakes to avoid.
Practice this topic
3 problems with answers.