Which of the following logarithmic expressions is undefined?
Practice Questions
Q1
Which of the following logarithmic expressions is undefined?
log_5(0)
log_5(1)
log_5(5)
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.