Concepts & Solved Examples
Learn the product, quotient, power, and base-changing properties with proofs and Examples 3 to 8.
Exercise 2.2 Solutions
Detailed step-by-step textbook solutions to all parts of Exercise 2.2 with interactive answer details.
Chapter Worksheets
Three levels (Easy, Medium, Hard) of worksheets targeting algebraic expansions and log simplifies.
Revision Notes
Formula cheat-sheet tables, De-Morgan-like log pitfalls, and base-10 rules.
Interactive Tests
Basic, Standard, and Advanced quizzes with 10 questions each to test your understanding of logarithmic laws.
What You'll Learn in This Section
Welcome to the core of logarithms! In this section, we will study and prove the algebraic laws of logarithms that simplify exponent operations. We will also learn about base-10 common logs used in Richter, decibel, and pH scales.
- Product Rule: $\log_a(MN) = \log_a(M) + \log_a(N)$ (turns multiplication into addition).
- Quotient Rule: $\log_a(M/N) = \log_a(M) - \log_a(N)$ (turns division into subtraction).
- Power Rule: $\log_a(M^k) = k \log_a(M)$ (exponent comes down).
- Change of Base: Converting base $a$ to any base $b$.
- Common Logarithms (Base 10): Real-world pH and decibel scale scales.
Start Learning
Click on Concepts & Solved Examples to begin studying the theory, or go straight to Exercise 2.2 Solutions to check your homework answers.