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Solve for a positive value of x. log_(x)(16)=2 Answer:

Solve for a positive value of x x .\newlinelog⁡x(16)=2 \log _{x}(16)=2 \newlineAnswer:

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Full solution

Q. Solve for a positive value of x x .\newlinelog⁡x(16)=2 \log _{x}(16)=2 \newlineAnswer:
  1. Understand the logarithmic equation: Understand the logarithmic equation.\newlineThe equation log⁡x(16)=2\log_{x}(16) = 2 means that xx raised to the power of 22 equals 1616.
  2. Convert to exponential equation: Convert the logarithmic equation to an exponential equation.\newlinex2=16x^2 = 16
  3. Solve for x: Solve for x by taking the square root of both sides.\newlinex2=16\sqrt{x^2} = \sqrt{16}
  4. Simplify the equation: Simplify the equation. x=±4x = \pm 4
  5. Choose positive solution: Since we are looking for the positive value of xx, we choose the positive solution.x=4x = 4

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