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If log_x(81) = 4, what is the value of x?

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Question: If log_x(81) = 4, what is the value of x?

Options:

  1. 3
  2. 4
  3. 9
  4. 16

Correct Answer: 3

Solution: 

log_x(81) = 4 implies x^4 = 81 => x = 3.

If log_x(81) = 4, what is the value of x?

Practice Questions

Q1
If log_x(81) = 4, what is the value of x?
  1. 3
  2. 4
  3. 9
  4. 16

Questions & Step-by-Step Solutions

If log_x(81) = 4, what is the value of x?
Correct Answer: 3
  • Step 1: Understand the equation log_x(81) = 4. This means that x raised to the power of 4 equals 81.
  • Step 2: Rewrite the equation in exponential form: x^4 = 81.
  • Step 3: To find x, we need to take the fourth root of 81. This means we need to find a number that, when multiplied by itself four times, equals 81.
  • Step 4: Calculate the fourth root of 81. We know that 3 * 3 = 9 and 9 * 9 = 81, so 3 raised to the power of 4 equals 81.
  • Step 5: Therefore, x = 3.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to find the base.
  • Exponential Form – Converting logarithmic expressions into exponential form to solve for the variable.
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