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Logarithms

ICSE · Class 9 · Mathematics

Flashcards for Logarithms — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

34 questions25 flashcards5 concepts

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An infographic summarizing the three main laws of logarithms: product rule, quotient rule, and power rule, with examples.
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25 Flashcards
Card 1Exponential and logarithmic form

Solve: 3^4 = 81. Write the same relation in logarithmic form.

Answer

Step 1: Use the equivalence a^b = c ⇔ log_a c = b. Step 2: Here, a = 3, b = 4, and c = 81. Step 3: So, log_3 81 = 4. Answer: log_3 81 = 4…

Card 2Exponential and logarithmic form

Convert to exponential form: log_2 0.125 = -3

Answer

Step 1: Use the equivalence log_a c = b ⇔ a^b = c. Step 2: Here, a = 2, b = -3, and c = 0.125. Step 3: So, 2^-3 = 0.125. Answer: 2^-3 = 0.125…

Card 3Common logarithms

Find: log_10 1000

Answer

Step 1: Write 1000 as a power of 10. Step 2: 1000 = 10^3. Step 3: So, log_10 1000 = 3. Check: 10^3 = 1000. Answer: 3…

Card 4Logarithms with negative powers

Find: log_3(1/9)

Answer

Step 1: Write 1/9 as a power of 3. Step 2: 1/9 = 3^-2. Step 3: So, log_3(1/9) = -2. Check: 3^-2 = 1/9. Answer: -2…

Card 5Solving simple logarithmic equations

Find x: log_2 x = -2

Answer

Step 1: Convert to exponential form. Step 2: 2^-2 = x. Step 3: Evaluate 2^-2 = 1/4. Answer: x = 1/4…

Card 6Solving logarithmic equations

Find x: log_4(x + 3) = 2

Answer

Step 1: Convert to exponential form. Step 2: 4^2 = x + 3. Step 3: 4^2 = 16, so x + 3 = 16. Step 4: x = 16 - 3 = 13. Answer: x = 13…

Card 7Product Law

When do you use the Product Law? Apply it to log_5(2 × 3).

Answer

Use the Product Law when the log is of a product. Formula: log_a(m × n) = log_a m + log_a n. Apply it here: log_5(2 × 3) = log_5 2 + log_5 3. This is valid because the expression is a product, not a s…

Card 8Product Law

Expand: log_a(m × n × p)

Answer

Step 1: Use the Product Law again and again. Step 2: log_a(m × n × p) = log_a m + log_a n + log_a p. Step 3: Each factor becomes a separate log term. Answer: log_a m + log_a n + log_a p…

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Frequently Asked Questions

What are the important topics in Logarithms for ICSE Class 9 Mathematics?
Logarithms covers several key topics that are frequently asked in ICSE Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Logarithms — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 34 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many flashcards are available for Logarithms?
There are 25 flashcards for Logarithms covering key definitions, formulas, and concepts. Use them daily for 10–15 minutes for best results.

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