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What is the domain of this logarithmic function? y=log⁡5(x−2)+7\newline y=\log_5(x-2)+7\newlineExpress the domain in inequality notation.

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Full solution

Q. What is the domain of this logarithmic function? y=log⁡5(x−2)+7\newline y=\log_5(x-2)+7\newlineExpress the domain in inequality notation.
  1. Identify Argument: First, identify the argument of the logarithm. Argument: x−2x - 2
  2. Set Up Inequality: The argument of the logarithm must be greater than 00. Set up the inequality: x - 2 > 0
  3. Solve for x: Solve the inequality for xx. x - 2 > 0 Add 22 to both sides: x > 2
  4. Find Domain: The domain of the function is all xx values greater than 22. So, the domain is: x > 2

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