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Which of the following logarithmic expressions is equivalent to log_10(0.01)?

Practice Questions

Q1
Which of the following logarithmic expressions is equivalent to log_10(0.01)?
  1. -2
  2. 2
  3. 0.01
  4. 1

Questions & Step-by-Step Solutions

Which of the following logarithmic expressions is equivalent to log_10(0.01)?
  • Step 1: Understand that log_10(0.01) means we want to find the power to which 10 must be raised to get 0.01.
  • Step 2: Recognize that 0.01 can be rewritten as a power of 10. Specifically, 0.01 is the same as 10 raised to the power of -2 (because 10^-2 = 0.01).
  • Step 3: Substitute 0.01 in the logarithmic expression with 10^-2. So, log_10(0.01) 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) simplifies to -2.
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