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Logarithms — Flashcards

ICSE · Class 9 · Mathematics

25 flashcards for Logarithms (ICSE Class 9 Mathematics) to test yourself on key terms and facts. Sample: "Solve: 3^4 = 81. Write the same relation"

34 questions25 flashcards21 formulas & key relations5 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·
Exponential and logarithmic formCommon logarithmsLogarithms with negative powersSolving simple logarithmic equationsSolving logarithmic equationsProduct Law
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?
Key topics in Logarithms include Meaning of Logarithm, Basic Values of Logarithms, Laws of Logarithms, Common Logarithms and Change of Base. Study these first, then practise questions on each for Class 9 exams.
How many flashcards are available for Logarithms?
There are 25 flashcards for Logarithms covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Logarithms for Class 9 exams?
Learn the core ideas first, then work through the 34 practice questions on Logarithms. Revise definitions regularly and use flashcards for quick recall before the exam.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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