📘 Review Exercise 2
Master Class 9 Mathematics Review Exercise 2 on Logarithms with comprehensive revision problems. This page includes free downloadable notes and complete solutions aligned with the PECTAA 2025 syllabus.
Quick Links:
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
Review Exercise 2 - Logarithms
This comprehensive review exercise covers all key concepts of logarithms including scientific notation, logarithmic forms, equation solving, and practical applications.
Review Exercise 2 provides a complete revision of the entire chapter on logarithms, testing students' understanding of all concepts covered in previous exercises. It serves as excellent preparation for examinations.
The exercise includes problems on scientific notation conversion, interconversion between exponential and logarithmic forms, simplification of logarithmic expressions, and real-world applications using logarithms.
Key Topics Covered in Review Exercise
- Scientific notation and ordinary notation conversion
- Interconversion between exponential and logarithmic forms
- Solving logarithmic and exponential equations
- Simplifying expressions as single logarithms
- Expanding logarithmic expressions using laws
- Calculations using logarithm tables
- Real-world applications of logarithms
Important Revision Points:
- Scientific Notation: \(a \times 10^n\) where \(1 \leq a < 10\)
- Logarithmic Form: If \(a^b = c\), then \(\log_a c = b\)
- Exponential Form: If \(\log_a c = b\), then \(a^b = c\)
- Remember: \(\log_a 1 = 0\) and \(\log_a a = 1\)
Real-World Applications
This review exercise includes practical applications that demonstrate the importance of logarithms in various fields:
- Population growth modeling using exponential functions
- Scientific calculations using logarithm tables for complex computations
- Financial mathematics applications in investment growth
Featured Problem: Population Growth
The exercise includes a practical problem where students use the population growth model \(p(t) = 22(1.025)^t\) to determine when a city's population will reach 35 million. This demonstrates the real-world application of logarithms in demographic studies and urban planning.
Students learn to set up the equation \(35 = 22(1.025)^t\) and solve for \(t\) using logarithmic properties, arriving at the solution that the population will reach 35 million in approximately 19 years (year 2035).
Created by Hira Science Academy | Aligned with PECTAA 2025 Syllabus