Which of the following is the correct simplification of log_2(8) + log_2(4)?

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Question: Which of the following is the correct simplification of log_2(8) + log_2(4)?

Options:

Correct Answer: log_2(16)

Solution:

Using the property of logarithms, log_2(8) + log_2(4) = log_2(8*4) = log_2(32) = log_2(16).

Which of the following is the correct simplification of log_2(8) + log_2(4)?

Which of the following is the correct simplification of log_2(8) + log_2(4)?

Step 1: Identify the logarithmic expressions: log_2(8) and log_2(4).
Step 2: Use the property of logarithms that states log_a(b) + log_a(c) = log_a(b*c).
Step 3: Apply this property to combine the two logarithms: log_2(8) + log_2(4) becomes log_2(8*4).
Step 4: Calculate the multiplication: 8 * 4 = 32.
Step 5: Now we have log_2(32).
Step 6: Recognize that 32 can be expressed as a power of 2: 32 = 2^5.
Step 7: Therefore, log_2(32) = 5.
Step 8: Check if log_2(8) + log_2(4) equals log_2(16).
Step 9: Note that 16 can also be expressed as a power of 2: 16 = 2^4.
Step 10: Therefore, log_2(16) = 4, which is not equal to log_2(32).

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