Problem 78 - College Algebra Essentials

Question

Find the domain of each logarithmic function. $$f(x)=\log (7-x)$$

Step-by-Step Solution

Answer

The domain of the logarithmic function \(f(x) = \log (7-x)\) is \(x < 7\).

Step 1: Identify the argument of the logarithmic function

The argument of the logarithmic function \(f(x) = \log (7-x)\) is \(7-x\).

Step 2: Set up inequality

Because the argument of a logarithm has to be greater than 0, we have the inequality \(7-x > 0\).

Step 3: Solve the inequality

To solve the inequality \(7-x > 0\), we will isolate x on one side by adding x to both sides and subtracting 0 from both sides, which yields \(x < 7\).