Which of the following logarithmic expressions is equivalent to log_3(81)?

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Question: Which of the following logarithmic expressions is equivalent to log_3(81)?

Options:

Correct Answer: 4

Solution:

Since 81 is 3^4, log_3(81) equals 4.

Which of the following logarithmic expressions is equivalent to log_3(81)?

Which of the following logarithmic expressions is equivalent to log_3(81)?

Step 1: Identify the base of the logarithm, which is 3 in this case.
Step 2: Rewrite the number 81 as a power of 3. Notice that 81 can be expressed as 3 raised to the power of 4 (3^4).
Step 3: Substitute 81 in the logarithmic expression with 3^4. This gives us log_3(3^4).
Step 4: Use the property of logarithms that states log_b(b^x) = x. Here, b is 3 and x is 4.
Step 5: Apply the property: log_3(3^4) equals 4.

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