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Which of the following expressions is equivalent to log_10(1/100)?

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Question: Which of the following expressions is equivalent to log_10(1/100)?

Options:

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

Correct Answer: -2

Solution: 

log_10(1/100) = log_10(10^-2) = -2.

Which of the following expressions is equivalent to log_10(1/100)?

Practice Questions

Q1
Which of the following expressions is equivalent to log_10(1/100)?
  1. -2
  2. 2
  3. 0
  4. -1

Questions & Step-by-Step Solutions

Which of the following expressions is equivalent to log_10(1/100)?
  • Step 1: Understand that log_10 means the logarithm base 10.
  • Step 2: Rewrite 1/100 as a power of 10. Since 100 is 10^2, we have 1/100 = 1/(10^2) = 10^-2.
  • Step 3: Now, substitute this back into the logarithm: log_10(1/100) becomes log_10(10^-2).
  • Step 4: Use the property of logarithms that states log_b(b^x) = x. Here, b is 10 and x is -2.
  • Step 5: Therefore, log_10(10^-2) = -2.
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