IGCSE Logarithms: Complete Guide for Cambridge IGCSE Mathematics

IGCSE logarithms are advanced algebra topics in Cambridge IGCSE Mathematics that appear in Paper 4 (Extended). Mastering logarithm rules, solving logarithmic equations, and logarithm properties is essential for achieving top grades in IGCSE exams.

This comprehensive IGCSE logarithms guide covers everything you need to know, including basic logarithm rules, solving equations, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to use logarithm rules, solve logarithmic equations, convert between exponential and logarithmic form, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Logarithms Matter

IGCSE logarithms are essential advanced algebra topics. Here’s why they’re so important:

• High frequency topic: Logarithm questions appear regularly in IGCSE Extended papers
• Foundation skill: Essential for advanced mathematics and calculus
• Exam weight: Typically worth 5-10 marks per paper
• Real-world applications: Used in science, engineering, and finance
• Problem-solving skills: Develops understanding of exponential relationships

Key insight from examiners: Students often struggle with logarithm rules or make errors when solving equations. This guide will help you master these systematically.

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Understanding Logarithms

Logarithm is the inverse of exponentiation.

If a^x = b, then log_a(b) = x

Example: 2³ = 8, so log₂(8) = 3

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Basic Logarithm Rules

Rule 1: Product Rule

log_a(xy) = log_a(x) + log_a(y)

Rule 2: Quotient Rule

log_a(x/y) = log_a(x) - log_a(y)

Rule 3: Power Rule

log_a(x^n) = n × log_a(x)

Rule 4: Change of Base

log_a(x) = log_b(x) / log_b(a)

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Common Logarithms

log₁₀(x) or log(x) - base 10 logarithm ln(x) - natural logarithm (base e)

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Solving Logarithmic Equations

Example 1: Solve log₂(x) = 3

Solution: Convert to exponential: x = 2³ = 8

Answer: x = 8

Example 2: Solve log(x) + log(3) = log(12)

Solution: Using product rule: log(3x) = log(12) Therefore: 3x = 12, so x = 4

Answer: x = 4

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Common Examiner Traps

• Rule application errors - Remember product, quotient, and power rules
• Base confusion - Check which base is being used
• Domain errors - Logarithms only defined for positive numbers

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Practice Questions

Question 1

Solve log₃(x) = 2

Solution: x = 3² = 9

Answer: x = 9

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Tutopiya Advantage: Personalised IGCSE Logarithms Coaching

• Live whiteboard walkthroughs of logarithm problems
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Frequently Asked Questions About IGCSE Logarithms

What is a logarithm?

A logarithm is the inverse of exponentiation. If a^x = b, then log_a(b) = x.

What are the main logarithm rules?

1. Product: log(xy) = log(x) + log(y)
2. Quotient: log(x/y) = log(x) - log(y)
3. Power: log(x^n) = n × log(x)

How do I solve logarithmic equations?

Use logarithm rules to simplify, then convert to exponential form if needed.

What is the difference between log and ln?

log is base 10, ln is natural logarithm (base e).

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Exponential Functions: Complete Guide - Master exponential functions
• IGCSE Graphs of Functions: Complete Guide - Master function graphs
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Logarithms with Tutopiya

Ready to excel in IGCSE logarithms? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
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Book a free IGCSE maths trial lesson and get personalized support to master logarithms and achieve your target grade.

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