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What is the value of log_10(0.01)?

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Question: What is the value of log_10(0.01)?

Options:

  1. -1
  2. -2
  3. 1
  4. 2

Correct Answer: -2

Solution: 

log_10(0.01) = log_10(10^-2) = -2.

What is the value of log_10(0.01)?

Practice Questions

Q1
What is the value of log_10(0.01)?
  1. -1
  2. -2
  3. 1
  4. 2

Questions & Step-by-Step Solutions

What is the value of log_10(0.01)?
  • Step 1: Understand what log_10 means. It is asking 'To what power do we raise 10 to get a certain number?'.
  • Step 2: Identify the number we are taking the log of, which is 0.01.
  • Step 3: Rewrite 0.01 in terms of powers of 10. We know that 0.01 is the same as 10 raised to the power of -2 (because 10^-2 = 1/10^2 = 1/100 = 0.01).
  • Step 4: Now we can rewrite the log expression: log_10(0.01) becomes log_10(10^-2).
  • Step 5: Use the property of logarithms that says log_b(b^x) = x. Here, b is 10 and x is -2.
  • Step 6: Therefore, log_10(10^-2) equals -2.
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