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ICSE Class 9 Algebra: logarithms — practice questions

Explore 28 free Algebra: logarithms questions in ICSE Class 9 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra: logarithms questions and exercises with answers

Showing questions 1–28 of 28.

Logarithm is mathematically defined as the inverse of what?Read the answer and worked solution →What is the log of 1 to any non-zero positive base b?Read the answer and worked solution →Evaluating log_b(b) for any permissible base yields which quantity?Read the answer and worked solution →Which number serves as the base for common logarithms?Read the answer and worked solution →Which mathematical constant is the base of natural logarithms?Read the answer and worked solution →What numerical base is used for binary logarithms?Read the answer and worked solution →Under the product rule, log_b(xy) is rewritten as which expression?Read the answer and worked solution →How does the quotient identity rewrite log_b(x/y)?Read the answer and worked solution →Applying the power law transforms log_b(x^p) into which form?Read the answer and worked solution →The logarithm of the p-th root of x can be stated as:Read the answer and worked solution →In the definition of log_b(x), what condition must base b satisfy?Read the answer and worked solution →In the real logarithm log_b(x), what restriction is placed on x?Read the answer and worked solution →What name is given to the fractional portion of a common logarithm?Read the answer and worked solution →The integer part of any common logarithm is given which name?Read the answer and worked solution →What is the change of base formula for log_b(x) using base k?Read the answer and worked solution →Which integer equals the base-2 logarithm of 16?Read the answer and worked solution →Find the value of x that satisfies log_2(x) = 5.Read the answer and worked solution →What sign do common logarithms of positive numbers under 1 have?Read the answer and worked solution →What is indicated when a bar is placed over the characteristic?Read the answer and worked solution →What is the characteristic of the common logarithm of 120?Read the answer and worked solution →Evaluating log_2(1/2) yields which numerical result?Read the answer and worked solution →If x = a * 10^n with 1 <= a < 10, what is the characteristic?Read the answer and worked solution →How is the digit count of integer x related to log10(x)?Read the answer and worked solution →Common logarithms are named Briggsian logarithms after whom?Read the answer and worked solution →Match each logarithmic statement with its equivalent exponential form:Read the answer and worked solution →Match each fundamental law of logarithms with its algebraic rule:Read the answer and worked solution →Match each special logarithmic property with its evaluated value:Read the answer and worked solution →Match each logarithm evaluation with its exact numerical answer:Read the answer and worked solution →

Worked practice questions

Logarithm is mathematically defined as the inverse of what?

  1. Multiplication
  2. Exponentiation
  3. Differentiation
  4. Factorisation
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Correct answer: B. Exponentiation

Logarithms represent the inverse mathematical operation of exponentiation.

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What is the log of 1 to any non-zero positive base b?

  1. 1
  2. b
  3. -1
  4. 0
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Correct answer: D. 0

Any non-zero base raised to the power of zero equals 1, so log_b(1) is always 0.

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Evaluating log_b(b) for any permissible base yields which quantity?

  1. 1
  2. 0
  3. b
  4. -1
Show answer and solution

Correct answer: A. 1

Raising the base b to the first power yields b, so log_b(b) equals 1.

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More Mathematics topics

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