Problem 99 - Introductory and Intermediate Algebra for College Students 4th

Question

Explain how to find the domain of a logarithmic function.

Step-by-Step Solution

Answer

To find the domain of a logarithmic function \( y = log_b(x) \), set \( x > 0 \) for the variable inside the logarithm leading to an inequality. Solve the inequality to get possible values for \( x \). These values represent the domain of the function. For the general logarithmic function, the domain will be \( (0, +\infty) \) as logarithm is only defined for positive numbers.

Step 1: Recognize the Logarithmic Function

Recall the general form of a logarithmic function which is \( y = log_b(x) \), where \( b > 0 \), \( b \neq 1 \), and \( x > 0 \). Set \( x > 0 \) leading to an inequality.

Step 2: Solve the inequality

Solving the inequality will provide the range of values \( x \) can take. This range of values is the domain of the logarithmic function. It's important to remember domain refers to all possible values of input \( x \) for the function \( f(x) \).

Step 3: Writing your Answer

Express the solution of your inequality as an interval. This interval is the domain of the logarithmic function. If \( x > 0 \), then the domain is \( (0, +\infty) \).