- 1. What Is a Logarithm?
Students will be able to state the meaning of a logarithm as an exponent and articulate the relationship between a base, a power, and a result.
- 2. Index Form ↔ Logarithm Form
Students will fluently convert any statement between index form and logarithm form in both directions, and use this conversion to solve for unknown values.
- 3. Special Logarithm Values
Students will recall and apply the four fundamental special values of logarithms to evaluate expressions instantly without complex calculation.
- 4. The Product Rule of Logarithms
Students will state and apply the product rule to combine or expand logarithms of products.
- 5. The Quotient Rule of Logarithms
Students will state and apply the quotient rule to combine or expand logarithms of fractions and quotients.
- 6. The Power Rule of Logarithms
Students will apply the power rule to bring exponents outside a logarithm as multipliers, and push coefficients inside as exponents.
- 7. Combining All Three Laws — Multi-Step Simplification
Students will solve multi-step logarithm simplification problems by selecting and sequencing the product, quotient, and power rules correctly.
- 8. Expressing Logs in Terms of Given Values
Students will decompose unfamiliar numbers into products and quotients of known prime factors (2, 3, 5, 7) and apply the three logarithm laws to express—and evaluate—logarithms in terms of given known values.
- 9. The Fundamental Identity
Students will derive and apply the fundamental identity a^{\log_a N} = N and its companion identity \log_a(a^x) = x to simplify numeric and algebraic expressions.
