Unit 3 · 4 lessons

Exponential & Logarithmic Functions

Logarithms from scratch — what a logarithm actually means, the laws that come straight from the exponent laws, the graph of the logarithm function and its transformations, and solving exponential and logarithmic equations (always checking for extraneous roots).

45 practice questions
34 flashcards
1 interactive lesson

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Lessons

1Introduction to LogarithmsA logarithm is an exponent. $lo g_{b} x$ answers the single question "what power of $b$ gives $x$ ?" — and that one sentence generates every rule in this unit.11 questions
2Laws of LogarithmsBecause a logarithm is an exponent, every exponent law becomes a logarithm law: products become sums, quotients become differences, and powers become multipliers.11 questions
3Graphs of Logarithmic Functions $y = lo g_{b} x$ is the inverse of $y = b^{x}$ , so it is that graph reflected in the line $y = x$ — turning the horizontal asymptote into a vertical one at $x = 0$ .Interactive11 questions
4Solving Exponential and Logarithmic EquationsTake the logarithm of both sides to free a variable from an exponent, condense to solve logarithmic equations — and always test every candidate root against the domain before accepting it.12 questions