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If log_3(27) = x, what is the value of x?

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Question: If log_3(27) = x, what is the value of x?

Options:

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Correct Answer: 3

Solution: 

Since 27 is 3^3, log_3(27) = 3.

If log_3(27) = x, what is the value of x?

Practice Questions

Q1
If log_3(27) = x, what is the value of x?
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Questions & Step-by-Step Solutions

If log_3(27) = x, what is the value of x?
  • Step 1: Understand that log_3(27) means 'to what power must 3 be raised to get 27?'
  • Step 2: Rewrite 27 as a power of 3. We know that 27 = 3^3.
  • Step 3: Now we can say log_3(27) = log_3(3^3).
  • Step 4: Use the property of logarithms that states log_b(b^a) = a. Here, b is 3 and a is 3.
  • Step 5: Therefore, log_3(3^3) = 3.
  • Step 6: Conclude that x = 3.
  • Logarithms – Understanding the relationship between exponents and logarithms, specifically how to express a number as a power of a base.
  • Base Conversion – Recognizing that 27 can be expressed as a power of 3, which is essential for solving logarithmic equations.
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