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What is the domain of this logarithmic function?y=log⁡4(x+5)−2\newline y=\log_4(x+5)-2\newlineExpress the domain in inequality notation.

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Q. What is the domain of this logarithmic function?y=log⁡4(x+5)−2\newline y=\log_4(x+5)-2\newlineExpress the domain in inequality notation.
  1. Identify argument: First, identify the argument of the logarithm: x+5 x + 5 .
  2. Check positivity: The argument x+5 x + 5 must be greater than 00 for the logarithm to be defined.
  3. Set up inequality: Set up the inequality: x + 5 > 0 .
  4. Solve for x: Solve for x x : x > -5 .
  5. Determine domain: The domain of the function is all x x such that x > -5 .

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