MathematicsChapter 2: Logarithms
Product, Quotient, Power
Product law: log(mn) = log m + log n.
Learning objectives
- Define and explain product, quotient, power.
- Apply product, quotient, power to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
Product law: log(mn) = log m + log n. Quotient law: log(m/n) = log m - log n. Power law: log(mk) = k log m. They follow from the index laws, because a logarithm is an exponent. Bases must match on every term. You may also write ln(mn) = ln m + ln n; the laws do not care which allowed base you chose.
Where / symbols
- Product, Quotient, Power
- Product law: log(mn) = log m + log n. Quotient law: log(m/n) = log m - log n. Power law: log(m^k) = k log m. They follow from the index laws, because a logarithm is an exponent. Bases must match on every term. You may also write ln(mn) = ln m + ln n; the laws do not care which allowed base you chose.
Relationship
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
Overview
Learn the idea, then use it:
Core Understanding
Product law: log(mn) = log m + log n. Quotient law: log(m/n) = log m - log n. Power law: log(mk) = k log m. They follow from the index laws, because a logarithm is an exponent. Bases must match on every term. You may also write ln(mn) = ln m + ln n; the laws do not care which allowed base you chose.
Examples log(mn) = log m + log n · log(m/n) = log m - log n · log(m^k) = k log m · PRODUCT, QUOTIENT, POWER: Product law: log(mn) = log m + log n. Quotient law: log(m/n) = log m - log n. Power law: log(m^k) = k log m. They follow
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — PRODUCT, QUOTIENT, POWER
Product law: log(mn) = log m + log n. Quotient law: log(m/n) = log m - log n. Power law: log(mk) = k log m. They follow from the index laws, because a logarithm is an exponent. Bases must match on every term. You may also write ln(mn) = ln m + ln n; the laws do not care which allowed base you chose.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge product, quotient, power with a neighbouring idea that uses a different definition, rule, or method.
Key points
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Product, Quotient, Power
Sticky Notes · Quick Revision
Core Idea
- Product law: log(mn) = log m + log n.
Key Points
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
Simple Check
- Explain product, quotient, power in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge product, quotient, power with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- Product law: log(mn) = log m + log n.
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
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