Which of the following is the correct simplification of log_10(1000) - log_10(10

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Question: Which of the following is the correct simplification of log_10(1000) - log_10(10)?

Options:

Correct Answer: 3

Solution:

Using the property of logarithms, log_10(1000) = 3 and log_10(10) = 1. Therefore, log_10(1000) - log_10(10) = 3 - 1 = 2.

Which of the following is the correct simplification of log_10(1000) - log_10(10)?

Which of the following is the correct simplification of log_10(1000) - log_10(10)?

Step 1: Identify the logarithm values. We need to find log_10(1000) and log_10(10).
Step 2: Calculate log_10(1000). Since 1000 is 10 raised to the power of 3 (10^3), log_10(1000) = 3.
Step 3: Calculate log_10(10). Since 10 is 10 raised to the power of 1 (10^1), log_10(10) = 1.
Step 4: Substitute the values into the expression. We have log_10(1000) - log_10(10) = 3 - 1.
Step 5: Perform the subtraction. 3 - 1 = 2.
Step 6: Conclude that the simplification of log_10(1000) - log_10(10) is 2.

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