Introduction
Assalam O Alaikum Dear Students and Respected Teachers Get Exercise 2.1 to 2.6 & Miscellaneous Exercise 2 Solved for the session 2026-27 | MCQs | Short Questions
Unit 2, Logarithms, comes right after Real Numbers in the Class 9 Mathematics FBISE New Book (NBF), and it leans heavily on the exponent rules from Unit 1. The chapter opens with a striking real-world hook: the 2005 Pakistan earthquake, measured 7.6 on the Richter scale and by the end of the unit, students actually understand what that number means and how it’s calculated using logarithms.
This chapter covers scientific notation, the definition of a logarithm, common and natural logarithms, characteristic and mantissa, log and antilog tables, the four laws of logarithms, and real-world applications like the Richter scale. It’s a compact unit, but an important one logarithms reappear throughout higher mathematics and science.
These notes have been prepared by the experienced faculty of HSA Notes, following the official FBISE (NBF) textbook and examination pattern.
Easy Concept Notes
Scientific Notation. Very large or very small numbers are written as d × 10ⁿ, where 1 ≤ d < 10. For example, the mass of Uranus (87 followed by 24 zeros) becomes a tidy 8.7 × 10²⁵ kg.
What is a Logarithm? If bʸ = x, then y is the logarithm of x with base b, written y = log_b x. A logarithm is simply an exponent in disguise — log_9 81 = 2 because 9² = 81.
Common vs Natural Logarithm. log x with no base written means base 10 (common logarithm, developed by Henry Briggs). ln x uses base e ≈ 2.71828 (natural logarithm, associated with John Napier).
Characteristic and Mantissa. A logarithm splits into two parts: characteristic (the whole-number part, found from scientific notation) and mantissa (the decimal part, read from a log table always positive).
The Four Laws of Logarithms
- Product Law: log_b (mn) = log_b m + log_b n
- Quotient Law: log_b (m/n) = log_b m − log_b n
- Power Law: log_b (mⁿ) = n log_b m
- Change of Base Law: log_a m = log_b m × log_a b
Nearly every question in Exercises 2.5 and 2.6 comes down to spotting which of these applies.
Topics Covered in Unit 2
- Scientific Notation
- Definition and Meaning of Logarithm
- Common Logarithm, Characteristic and Mantissa
- Antilogarithm
- Natural Logarithm
- Laws of Logarithms (Product, Quotient, Power, Change of Base)
- Applications of Logarithms (Richter Scale)
Importance of Unit 2
Logarithms connect back to exponents from Unit 1 and forward to exponential equations later on. A student comfortable with the log–exponent relationship will find those topics far less intimidating.
Exercise 2.1 Solved
Converting numbers between standard and scientific notation, including real-world quantities like light-year distances and the speed of light. Full step-by-step solutions are in the uploaded notes.
Exercise 2.2 Solved
Checking whether a logarithm is defined, and converting between exponential and logarithmic form. This is where the core definition gets tested from every angle.
Exercise 2.3 Solved
Finding the logarithm of a number using scientific notation, characteristic, and the log table — the mechanical skill that everything later in the unit depends on.
Exercise 2.4 Solved
Finding the antilog of a number using the antilog table, and locating the decimal point correctly using the characteristic.
Exercise 2.5 Solved
Applying the product, quotient, power, and change-of-base laws to expand, combine, and evaluate logarithmic expressions often several laws in the same question.
Exercise 2.6 Solved
Finding the number of digits in large powers, evaluating complex expressions by taking logs and antilogs, and applying the Richter scale formula to compare earthquake intensities.
Miscellaneous Exercise
A large MCQ-heavy review covering every idea in the unit: scientific notation, defined vs undefined logs, characteristic and mantissa, all four laws, and conversions — a solid way to confirm the unit has properly sunk in before the exam.
Sample Solved Questions
A taste of the kind of step-by-step working included in the full notes:
Q1 (Exercise 2.3 style). Find log 156.3. Write 156.3 in scientific notation: 1.563 × 10². So characteristic = 2. Looking up 1563 in the log table gives mantissa = 0.1939. Therefore log 156.3 = 2 + 0.1939 = 2.1939.
Q2 (Exercise 2.5 style). Use the laws of logarithms to expand log(5p²q^½ / 4√(st³)). Apply the quotient law, then the product law, then the power law: = log 5 + 2 log p + ½ log q − log 4 − ½ log s − 3 log t.
Q3 (Exercise 2.6 style, Richter Scale). An earthquake measuring 8.2 is how many times stronger than one measuring 7.6? Using M = log(I/I₀), the difference in magnitude gives log(I₂/I₁) = 0.6, so I₂/I₁ = antilog 0.6 ≈ 4 — meaning it’s roughly four times stronger.
For Teachers
If you’re teaching this unit, the Richter-scale example at the start makes a natural hook for opening a lesson it gives students a concrete reason to care about logarithms before the notation even appears. The notes are organized exercise-by-exercise, so individual sections can be pulled out directly for classwork, homework sheets, or quiz preparation without needing to rebuild anything from scratch. The MCQ bank and short questions are also grouped by concept, which makes it easy to assemble a quick class test focused on just one or two ideas say, characteristic and mantissa, or the four laws — rather than the whole chapter at once.
Class 9 Unit 2 Notes
Our notes include:
- Easy Concept Notes
- Solved Examples
- Complete Exercise 2.1 to 2.6 Solutions
- Miscellaneous Exercise Solutions
- Important Definitions
- Formula Summary
- Board Tips
Class 9 Unit 2 MCQs
- Chapter-wise MCQs
- Conceptual MCQs
- Board-style Multiple Choice Questions
- Answer Keys with Explanations
The Miscellaneous Exercise alone has 18 MCQs, so this unit is a favorite for objective-paper testing extra MCQ practice pays off here for students, and the ready-made answer keys save teachers time when building a quick class quiz.
Short Questions
Covering the definition of a logarithm, checking whether a log is defined, the four laws, common vs natural logarithms, and characteristic/mantissa — prepared according to the latest FBISE examination pattern.
Long Questions
Complete step-by-step solutions following the official textbook method, so students can see exactly how marks are distributed.
Sample Papers
Board-style Sample Papers for revision and timing practice ahead of the exam.
Easy Notes
Complete Unit 2 PDF Notes include Solved Exercises, MCQs, Short Questions, Long Questions, Guess Papers, Sample Papers, Formula Sheet, and Quick Revision Notes.
Online Classes
Prefer live teaching over self-study? HSA Notes also offers online classes contact hsanotes48@gmail.com for Class 9.
Frequently Asked Questions
What is a logarithm in simple words? A logarithm tells you what power a base number needs to be raised to, to get another number. Since 2³ = 8, log base 2 of 8 is 3.
How many exercises are in Unit 2 of Class 9 Math (NBF)? Six exercises 2.1 through 2.6 plus a Miscellaneous Exercise at the end.
Do I need a calculator for this unit? No, the FBISE syllabus expects students to use log tables and antilog tables by hand, which is exactly what this unit teaches.
Can teachers use these notes for classroom teaching? Yes, the exercise-by-exercise breakdown, formula summary, and MCQ bank are designed so a teacher can lift a section directly into a lesson plan, worksheet, or class test without extra prep work.
Conclusion
Unit 2: Logarithms is short but foundational it reinforces the exponent work from Unit 1 and sets up ideas that return throughout higher mathematics. Working through Exercise 2.1 to 2.6, the Miscellaneous Exercise, MCQs, short questions, long questions, and sample papers gives students a solid grip on logarithms and real confidence heading into the FBISE board examination and gives teachers a ready set of material to build lessons and assessments around.