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

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

Options:

  1. a^x
  2. x^a
  3. log_a(x)
  4. a * x

Correct Answer: a^x

Solution: 

By the definition of logarithms, if log_a(b) = x, then b = a^x.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If log_a(b) = x, which of the following is equivalent to b?
  • Step 1: Understand what log_a(b) means. It means 'to what power do we raise a to get b'.
  • Step 2: Identify the equation given: log_a(b) = x.
  • Step 3: Rewrite the logarithmic equation in exponential form. This means we can express b as a raised to the power of x.
  • Step 4: Write the equivalent expression: b = a^x.
  • Step 5: Confirm that this is the correct transformation based on the definition of logarithms.
  • Logarithmic Definition – Understanding that the logarithm log_a(b) = x means that b is equal to a raised to the power of x.
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