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If log_3(81) = x, what is the value of x?

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Question: If log_3(81) = x, what is the value of x?

Options:

  1. 3
  2. 4
  3. 5
  4. 6

Correct Answer: 4

Solution: 

log_3(81) = log_3(3^4) = 4.

If log_3(81) = x, what is the value of x?

Practice Questions

Q1
If log_3(81) = x, what is the value of x?
  1. 3
  2. 4
  3. 5
  4. 6

Questions & Step-by-Step Solutions

If log_3(81) = x, what is the value of x?
  • Step 1: Understand that log_3(81) means 'to what power must 3 be raised to get 81'.
  • Step 2: Rewrite 81 as a power of 3. We know that 3^4 = 81.
  • Step 3: Now we can say log_3(81) = log_3(3^4).
  • Step 4: Use the property of logarithms that states log_b(a^c) = c * log_b(a).
  • Step 5: Apply this property: log_3(3^4) = 4 * log_3(3).
  • Step 6: Since log_3(3) = 1 (because 3^1 = 3), we have 4 * 1 = 4.
  • Step 7: Therefore, log_3(81) = 4, so x = 4.
  • Logarithms – Understanding how to express numbers in terms of their logarithmic base and exponent.
  • Exponents – Recognizing that 81 can be expressed as a power of 3 (3^4).
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