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

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

Options:

Correct Answer: -2

Solution:

log_10(0.01) can be rewritten as log_10(10^-2) = -2.

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

Which of the following 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: Rewrite 0.01 as a fraction: 0.01 = 1/100.
Step 3: Recognize that 100 can be written as 10^2, so 0.01 can be rewritten as 1/(10^2).
Step 4: Use the property of exponents: 1/(10^2) = 10^-2.
Step 5: Now we have log_10(0.01) = log_10(10^-2).
Step 6: Use the property of logarithms: log_b(b^x) = x. Here, b is 10 and x is -2.
Step 7: Therefore, log_10(10^-2) = -2.

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