Problem 47 - Introductory and Intermediate Algebra for College Students 4th

Question

Find the domain of each logarithmic function. $$f(x)=\log _{5}(x+4)$$

Step-by-Step Solution

Answer

The domain of the function \(f(x)=\log _{5}(x+4)\) is \(x > -4\). This is the set of all real numbers greater than -4.

Step 1: Set the argument of the logarithm greater than zero

To find the domain, you must determine which values for the variable \(x\) will make the expression inside the logarithm positive. All those values together will make up the domain of the function. Therefore, write down the following inequality: \(x+4 > 0\).

Step 2: Solve for x

Now, solve this inequality for \(x\). Subtract 4 from both sides: \(x > -4\). This means that \(x\), that satisfies the function, is any real number greater than -4.