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If log_x(81) = 4, find x.

Practice Questions

Q1
If log_x(81) = 4, find x.
  1. 3
  2. 4
  3. 5
  4. 9

Questions & Step-by-Step Solutions

If log_x(81) = 4, find x.
Correct Answer: 3
  • Step 1: Start with the equation log_x(81) = 4.
  • Step 2: Understand that log_x(81) = 4 means that x raised to the power of 4 equals 81.
  • Step 3: Rewrite the equation as x^4 = 81.
  • Step 4: Recognize that 81 can be expressed as 3 raised to the power of 4, so rewrite the equation as x^4 = 3^4.
  • Step 5: Since the bases are the same (both are raised to the power of 4), we can set the bases equal to each other: x = 3.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to find the base.
  • Exponential Equations – Converting logarithmic forms to exponential forms to solve for the variable.
  • Properties of Exponents – Using properties of exponents to simplify and solve equations.
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