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What is the domain of this logarithmic function? y=log⁡3(x+9)+1\newline y=\log_3(x+9)+1\newlineExpress the domain in inequality notation.

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Full solution

Q. What is the domain of this logarithmic function? y=log⁡3(x+9)+1\newline y=\log_3(x+9)+1\newlineExpress the domain in inequality notation.
  1. Identify Argument: First, identify the argument of the logarithm. Argument: x+9x + 9
  2. Set Inequality: Set the argument greater than 00 because the logarithm is only defined for positive numbers. x + 9 > 0
  3. Solve for xx: Solve the inequality for xx. x + 9 > 0 x > -9
  4. Find Domain: The domain of the function is all xx values greater than −9-9. Domain: x > -9

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