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Which of the following is true for log_10(0.1)?

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Question: Which of the following is true for log_10(0.1)?

Options:

  1. -1
  2. 0
  3. 1
  4. 10

Correct Answer: -1

Solution: 

log_10(0.1) = log_10(10^-1) = -1.

Which of the following is true for log_10(0.1)?

Practice Questions

Q1
Which of the following is true for log_10(0.1)?
  1. -1
  2. 0
  3. 1
  4. 10

Questions & Step-by-Step Solutions

Which of the following is true for log_10(0.1)?
  • Step 1: Understand what log_10(0.1) means. It asks for the power to which 10 must be raised to get 0.1.
  • Step 2: Rewrite 0.1 as a power of 10. We know that 0.1 is the same as 10 raised to the power of -1, so we can write it as 0.1 = 10^-1.
  • Step 3: Substitute this back into the logarithm. Now we have log_10(0.1) = log_10(10^-1).
  • Step 4: Use the property of logarithms that states log_b(b^x) = x. Here, b is 10 and x is -1.
  • Step 5: Apply the property: log_10(10^-1) = -1.
  • Step 6: Conclude that log_10(0.1) = -1.
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