Problem 76 - College Algebra Essentials

Question

Find the domain of each logarithmic function. $$f(x)=\log _{5}(x+6)$$

Step-by-Step Solution

Answer

The domain of the function is \(x > -6\).

Step 1: Set up the inequality

Considering the properties of logarithms, to find the domain of the function we need to set up an inequality where \(x + 6 > 0\). This is because a logarithm is defined only for positive numbers.

Step 2: Solve the inequality

Solving the inequality \(x + 6 > 0\) for x, we would subtract 6 from both sides, which gives us \(x > -6\).

Step 3: The Domain

With \(x > -6\), we find that the domain of the given function is all real numbers greater than -6.