📘 Exercise 2.4
Learn and practice Class 9 Mathematics Exercise 2.4 on Logarithms with step-by-step solutions. This page includes free downloadable notes and solved examples aligned with the PECTAA 2025 syllabus.
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Chapter 1
Real Numbers
Chapter 2
Logarithms
Chapter 3
Sets and Functions
Chapter 4
Factorization and Algebraic Manipulation
Chapter 5
Linear Equations and Inequalities
Chapter 6
Trigonometry
Chapter 7
Coordinate Geometry
Chapter 8
Logic
Chapter 9
Similar Figures
Chapter 10
Graphs of Functions
Chapter 11
Loci and Construction
Chapter 12
Information Handling
Chapter 13
Probability
Exercise 2.4 - Logarithms
This exercise focuses on applying logarithm laws, simplifying logarithmic expressions, solving logarithmic equations, and using logarithms in real-world applications.
Exercise 2.4 provides practice problems that help students master the laws of logarithms, including product rule, quotient rule, and power rule. Students will learn to simplify complex logarithmic expressions and solve equations involving logarithms.
The exercise covers logarithmic calculations without calculators, conversion between logarithmic forms, and practical applications of logarithms in fields like earthquake measurement and financial calculations.
Key Topics Covered
- Evaluating logarithmic expressions without calculators
- Writing expressions as single logarithms
- Expanding logarithmic expressions using laws
- Solving logarithmic equations
- Using logarithm tables for calculations
- Real-world applications of logarithms
Important Logarithm Laws:
- Product Rule: \(\log_a(mn) = \log_a m + \log_a n\)
- Quotient Rule: \(\log_a\left(\frac{m}{n}\right) = \log_a m - \log_a n\)
- Power Rule: \(\log_a(m^n) = n \log_a m\)
- Change of Base: \(\log_a b = \frac{\log_c b}{\log_c a}\)
Real-World Applications
This exercise includes practical applications of logarithms such as:
- Earthquake magnitude calculation using the Richter scale formula
- Compound interest problems to determine investment growth over time
- Scientific calculations using logarithm tables