Which of the following is the correct simplification of log_5(25) - log_5(5)?

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Question: Which of the following is the correct simplification of log_5(25) - log_5(5)?

Options:

Correct Answer: 1

Solution:

log_5(25) = 2 and log_5(5) = 1, thus log_5(25) - log_5(5) = 2 - 1 = 1.

Which of the following is the correct simplification of log_5(25) - log_5(5)?

Which of the following is the correct simplification of log_5(25) - log_5(5)?

Step 1: Identify the logarithm log_5(25). This means we are looking for the power to which 5 must be raised to get 25.
Step 2: Since 5^2 = 25, we find that log_5(25) = 2.
Step 3: Next, identify the logarithm log_5(5). This means we are looking for the power to which 5 must be raised to get 5.
Step 4: Since 5^1 = 5, we find that log_5(5) = 1.
Step 5: Now, we can substitute the values we found into the expression: log_5(25) - log_5(5) becomes 2 - 1.
Step 6: Finally, calculate 2 - 1, which equals 1.

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