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What is the value of log_3(81)?
What is the value of log_3(81)?
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Practice Questions
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What is the value of log_3(81)?
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log_3(81) = log_3(3^4) = 4.
Questions & Step-by-step Solutions
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Q: What is the value of log_3(81)?
Solution:
log_3(81) = log_3(3^4) = 4.
Steps: 6
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Step 1: Understand that log_3(81) means 'to what power must 3 be raised to get 81?'
Step 2: Recognize that 81 can be written as a power of 3. Specifically, 81 = 3^4.
Step 3: Rewrite the logarithm using this power: log_3(81) = 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 this property: log_3(3^4) = 4.
Step 6: Conclude that the value of log_3(81) is 4.
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