Problem 75 - College Algebra Essentials

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 \(x>-4\).

Step 1: Understanding the logarithm argument

In the given function \(f(x)=\log _{5}(x+4)\), the argument of the logarithm is \(x+4\).

Step 2: Setting the constraint

For a logarithmic function, the argument must be greater than zero. So, we set \(x+4\) greater than zero to solve for the domain.

Step 3: Finding the domain

Solving the inequality \(x+4>0\), we subtract 4 from both sides, which gives us: \(x>-4\). Hence, the domain of the function is all real numbers greater than -4.