Problem

Find the domain of the logarithmic function. \[ f(x)=\ln (8-x) \] (- (A) , 8) or $(8$, ) (- B .0) (c) $(-$ ,8) $(-8$, (D)

Solution

Step 1 :Find the domain of the logarithmic function: \(f(x)=\ln (8-x)\)

Step 2 :Since the natural logarithm is only defined for positive numbers, we need to find the values of x that will make the expression inside the logarithm \((8-x)\) positive.

Step 3 :Solve the inequality: \(8-x > 0\)

Step 4 :Add x to both sides: \(8 > x\)

Step 5 :Final Answer: \(\boxed{(-\infty, 8)}\)

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Source: https://solvelyapp.com/problems/16073/

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