Which of the following logarithmic expressions is undefined?

Practice Questions

Q1
Which of the following logarithmic expressions is undefined?
  1. log_5(0)
  2. log_5(1)
  3. log_5(5)
  4. log_5(25)

Questions & Step-by-Step Solutions

Which of the following logarithmic expressions is undefined?
  • Step 1: Understand what a logarithm is. A logarithm answers the question: 'To what power must a certain number (the base) be raised to get another number?'
  • Step 2: Identify the base of the logarithm in the expression log_5(0). Here, the base is 5.
  • Step 3: Recognize that logarithms can only take positive numbers as their input. This means you cannot take the logarithm of zero or a negative number.
  • Step 4: Since the input in log_5(0) is zero, this expression is not valid.
  • Step 5: Conclude that log_5(0) is undefined because you cannot find a power that 5 can be raised to in order to equal zero.
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