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

Practice Questions

Q1
If logx(81) = 4, what is the value of x?
  1. 3
  2. 4
  3. 5
  4. 6

Questions & Step-by-Step Solutions

If logx(81) = 4, what is the value of x?
Correct Answer: 3
  • Step 1: Understand the equation logx(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 can be written as x = 81^(1/4).
  • Step 4: Calculate the fourth root of 81. Since 81 is 3^4, we have 81^(1/4) = (3^4)^(1/4) = 3.
  • Step 5: Therefore, the value of x is 3.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to solve for the base.
  • Exponents – Applying exponent rules to find the value of x from the logarithmic equation.
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