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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.
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Product, Quotient, Power
What is it?
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.
In simple words
- 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
Important terms
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.
What you should learn
- 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.
Examples
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
CORE UNDERSTANDING
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.
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Recommended for Class 9
Full school-level explanation
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.
Learn the idea, then use it:
WHAT — 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.
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.
CORE UNDERSTANDING
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.
Remember
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
Examples
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = 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.
Remember
- correct term
- chapter link
- clear application
Examples
- Define first
- Show the rule or evidence
- Check units, labels, and conclusion
Remember
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
- keep the ideas separate
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
- correct term
Deeper understanding
Go beyond memorising Product, Quotient, Power. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
Key Points
Simple Check
How to Answer
Exam focus
Quick revision
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
- keep the ideas separate
- 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) =
- WHAT — 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) =
Do not merge product, quotient, power with a neighbouring idea that uses a different definition, rule, or method.
For long answers on Product, Quotient, Power: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
- keep the ideas separate
Important formulas
- log(mn) = log m + log n
- log(m/n) = log m - log n
- log(mk) = k log m
Common exam traps
- Do not merge product, quotient, power with a neighbouring idea that uses a different definition, rule, or method.
- Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not merge product, quotient, power with a neighbouring idea that uses a different definition, rule, or method.
- Mistake
Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
- Mistake
Do not merge product, quotient, power with a neighbouring idea that uses a different definition, rule, or method.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
log(mn) = log m + log n
log(m/n) = log m - log n
log(mk) = k log m
keep the ideas separate
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 logarith
log(mn) = log m + log n
- Definition
- 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 logarith
- Formula
- log(mn) = log m + log n
- Example
- log(mn) = log m + log n
- Critical warning
- Do not merge product, quotient, power with a neighbouring idea that uses a different definition, rule, or method.
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Exam Practice
Define
Q1. Define Product, Quotient, Power.
Explain
Q2. Explain: CORE UNDERSTANDING.
Example
Q3. Give one clear example of Product, Quotient, Power and say why it fits.
Mistake
Q4. State one common mistake students make about Product, Quotient, Power.
Exam note
Q5. Write a short exam note on Product, Quotient, Power: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.