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If log_a(b) = c, which of the following is equivalent?

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Question: If log_a(b) = c, which of the following is equivalent?

Options:

  1. a^c = b
  2. b^c = a
  3. c^a = b
  4. b^a = c

Correct Answer: a^c = b

Solution: 

The definition of logarithms states that if log_a(b) = c, then a raised to the power of c equals b, hence a^c = b.

If log_a(b) = c, which of the following is equivalent?

Practice Questions

Q1
If log_a(b) = c, which of the following is equivalent?
  1. a^c = b
  2. b^c = a
  3. c^a = b
  4. b^a = c

Questions & Step-by-Step Solutions

If log_a(b) = c, which of the following is equivalent?
  • Step 1: Understand the notation log_a(b) = c. This means 'a raised to the power of c equals b'.
  • Step 2: Rewrite the equation using the definition of logarithms. Change log_a(b) = c to a^c = b.
  • Step 3: Recognize that a^c is the same as saying 'a raised to the power of c'.
  • Step 4: Conclude that if log_a(b) = c, then the equivalent expression is a^c = b.
  • Logarithmic Definition – Understanding that the logarithm log_a(b) = c means that a^c = b.
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