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What is the base of the logarithm if log_2(8) = 3?

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Question: What is the base of the logarithm if log_2(8) = 3?

Options:

  1. 2
  2. 3
  3. 4
  4. 8

Correct Answer: 2

Solution: 

Since 8 is 2 raised to the power of 3 (2^3 = 8), the base of the logarithm is 2.

What is the base of the logarithm if log_2(8) = 3?

Practice Questions

Q1
What is the base of the logarithm if log_2(8) = 3?
  1. 2
  2. 3
  3. 4
  4. 8

Questions & Step-by-Step Solutions

What is the base of the logarithm if log_2(8) = 3?
  • Step 1: Understand what log_2(8) means. It asks, 'To what power do we raise 2 to get 8?'
  • Step 2: Recognize that 8 can be written as a power of 2. Specifically, 8 = 2^3.
  • Step 3: Since 2 raised to the power of 3 equals 8, we can say that log_2(8) = 3.
  • Step 4: Identify the base of the logarithm. In this case, the base is 2.
  • Logarithmic Functions – Understanding the relationship between exponents and logarithms, specifically how to identify the base of a logarithm.
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