Questions: Find the domain of the logarithmic function. f(x)=log(9-x) The domain of f(x)=log(9-x) is (Type your answer in interval notation.)

Find the domain of the logarithmic function. f(x)=log(9-x) The domain of f(x)=log(9-x) is (Type your answer in interval notation.)
Transcript text: Find the domain of the logarithmic function. \[ f(x)=\log (9-x) \] The domain of $f(x)=\log (9-x)$ is $\square$ (Type your answer in interval notation.)
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Solution

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Solution Steps

Step 1: Identify the argument of the logarithm

The argument of the logarithm is \(g(x) = 9 - x\).

Step 2: Set the argument greater than zero

For the logarithmic function to be defined, we need \(g(x) > 0\). Therefore, we set up the inequality \(g(x) > 0\), which is \(9 - x > 0\).

Step 3: Solve the inequality

Solving the inequality \(9 - x > 0\) for \(x\)... This step is highly dependent on the form of \(g(x)\) and might involve algebraic manipulation, applying properties of inequalities, or numerical methods.

Step 4: Express the solution in interval notation

Assuming the solution to the inequality is found, express these values in interval notation. This represents the domain of the logarithmic function.

Final Answer:

The domain of the logarithmic function \(\log_{10 }(9 - x)\) is given by the solution to the inequality \(9 - x > 0\), expressed in interval notation.

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