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If log_x(27) = 3, find x.

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Question: If log_x(27) = 3, find x.

Options:

  1. 3
  2. 9
  3. 27
  4. 81

Correct Answer: 9

Solution: 

log_x(27) = 3 implies x^3 = 27 => x = 3.

If log_x(27) = 3, find x.

Practice Questions

Q1
If log_x(27) = 3, find x.
  1. 3
  2. 9
  3. 27
  4. 81

Questions & Step-by-Step Solutions

If log_x(27) = 3, find x.
Correct Answer: 3
  • Step 1: Understand the equation log_x(27) = 3. This means that x raised to the power of 3 equals 27.
  • Step 2: Rewrite the equation in exponential form: x^3 = 27.
  • Step 3: To find x, we need to solve the equation x^3 = 27.
  • Step 4: Take the cube root of both sides of the equation: x = 27^(1/3).
  • Step 5: Calculate the cube root of 27. Since 3 * 3 * 3 = 27, we find that 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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