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

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

Options:

Correct Answer: -2

Solution:

Since 0.01 is 10^-2, log_10(0.01) = -2.

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

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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