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If log_3(x) = 4, what is the value of x?

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Question: If log_3(x) = 4, what is the value of x?

Options:

  1. 27
  2. 81
  3. 243
  4. 729

Correct Answer: 243

Solution: 

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

If log_3(x) = 4, what is the value of x?

Practice Questions

Q1
If log_3(x) = 4, what is the value of x?
  1. 27
  2. 81
  3. 243
  4. 729

Questions & Step-by-Step Solutions

If log_3(x) = 4, what is the value of x?
  • Step 1: Understand that log_3(x) = 4 means that 3 raised to the power of 4 equals x.
  • Step 2: Write the equation in exponential form: x = 3^4.
  • Step 3: Calculate 3^4, which means 3 multiplied by itself 4 times: 3 * 3 * 3 * 3.
  • Step 4: First, calculate 3 * 3 = 9.
  • Step 5: Next, multiply 9 by 3: 9 * 3 = 27.
  • Step 6: Finally, multiply 27 by 3: 27 * 3 = 81.
  • Step 7: Therefore, the value of x is 81.
  • Logarithms – Understanding the relationship between logarithms and exponents, specifically how to convert from logarithmic form to exponential form.
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