If log_5(25) + log_5(5) = x, what is the value of x?

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Question: If log_5(25) + log_5(5) = x, what is the value of x?

Options:

Correct Answer: 3

Solution:

log_5(25) = 2 and log_5(5) = 1. Therefore, x = 2 + 1 = 3.

If log_5(25) + log_5(5) = x, what is the value of x?

If log_5(25) + log_5(5) = x, what is the value of x?

Step 1: Identify the logarithm log_5(25).
Step 2: Recognize that 25 is 5 raised to the power of 2 (5^2).
Step 3: Use the property of logarithms that states log_b(b^a) = a. Therefore, log_5(25) = 2.
Step 4: Identify the logarithm log_5(5).
Step 5: Recognize that 5 is 5 raised to the power of 1 (5^1).
Step 6: Use the same property of logarithms. Therefore, log_5(5) = 1.
Step 7: Add the results from Step 3 and Step 6: 2 + 1.
Step 8: Calculate the sum: 2 + 1 = 3.
Step 9: Conclude that x = 3.

Logarithmic Properties – Understanding the properties of logarithms, specifically that log_b(b^a) = a and log_b(b) = 1.
Base Conversion – Recognizing that 25 can be expressed as 5^2, which simplifies the logarithmic calculation.