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If log_a(1) = 0, what can be said about the value of a? (2019)

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Question: If log_a(1) = 0, what can be said about the value of a? (2019)

Options:

  1. a > 0
  2. a < 0
  3. a = 1
  4. a = 0

Correct Answer: a = 1

Exam Year: 2019

Solution: 

log_a(1) = 0 is true for any base a > 0, except when a = 1.

If log_a(1) = 0, what can be said about the value of a? (2019)

Practice Questions

Q1
If log_a(1) = 0, what can be said about the value of a? (2019)
  1. a > 0
  2. a < 0
  3. a = 1
  4. a = 0

Questions & Step-by-Step Solutions

If log_a(1) = 0, what can be said about the value of a? (2019)
  • Step 1: Understand what log_a(1) means. It represents the logarithm of 1 with base a.
  • Step 2: Recall the definition of logarithms: log_a(b) = c means a^c = b.
  • Step 3: Apply this definition to log_a(1) = 0. This means a^0 = 1.
  • Step 4: Remember that any number raised to the power of 0 equals 1, as long as the base is not zero.
  • Step 5: Conclude that log_a(1) = 0 is true for any base a that is greater than 0, except when a = 1, because 1^0 = 1.
  • Logarithmic Properties – Understanding that the logarithm of 1 in any base is always 0, except when the base is 1.
  • Base of Logarithm – Recognizing the conditions under which a logarithm is defined, particularly the restrictions on the base.
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