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If log_b(x) = y, which of the following statements is true?

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Question: If log_b(x) = y, which of the following statements is true?

Options:

  1. b^y = x
  2. y^b = x
  3. x^b = y
  4. b^x = y

Correct Answer: b^y = x

Solution: 

The definition of logarithms states that if log_b(x) = y, then b raised to the power of y equals x, hence b^y = x.

If log_b(x) = y, which of the following statements is true?

Practice Questions

Q1
If log_b(x) = y, which of the following statements is true?
  1. b^y = x
  2. y^b = x
  3. x^b = y
  4. b^x = y

Questions & Step-by-Step Solutions

If log_b(x) = y, which of the following statements is true?
  • Step 1: Understand the notation log_b(x) = y. This means 'the logarithm of x with base b equals y'.
  • Step 2: Recall the definition of logarithms. It states that if log_b(x) = y, then b raised to the power of y equals x.
  • Step 3: Write this relationship in mathematical form: b^y = x.
  • Step 4: Recognize that this means if you take the base b and raise it to the exponent y, you will get x.
  • Logarithmic Definition – Understanding that the logarithm log_b(x) = y means that b^y = x.
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