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What is the base of the logarithm if log_b(1) = 0?

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Question: What is the base of the logarithm if log_b(1) = 0?

Options:

  1. Any positive number
  2. 1
  3. 0
  4. Undefined

Correct Answer: Any positive number

Solution: 

For any base b > 0, log_b(1) = 0, since b^0 = 1.

What is the base of the logarithm if log_b(1) = 0?

Practice Questions

Q1
What is the base of the logarithm if log_b(1) = 0?
  1. Any positive number
  2. 1
  3. 0
  4. Undefined

Questions & Step-by-Step Solutions

What is the base of the logarithm if log_b(1) = 0?
  • Step 1: Understand what a logarithm is. A logarithm log_b(x) answers the question: 'To what power must we raise b to get x?'
  • Step 2: In the equation log_b(1) = 0, we are trying to find the base b such that when we raise b to the power of 0, we get 1.
  • Step 3: Recall the property of exponents: any number raised to the power of 0 equals 1. This means b^0 = 1 for any base b that is greater than 0.
  • Step 4: Since log_b(1) = 0 holds true for any base b > 0, we conclude that the base of the logarithm can be any positive number.
  • Logarithmic Identity – The logarithm of 1 in any base is always 0, as any number raised to the power of 0 equals 1.
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