Find the domain (in interval notation) of a logarithm function, examples part 3

TL;DR

Learn how to find the domain of logarithmic functions by setting up inequalities and using a number line.

Transcript

two more examples on how to find the domain of a function specifically log functions in this case we have f ofx is equal to Ln of 1 / x - 5 and keep in mind Ln is just log base e so the same principle here applies let me make sure let me write it down here whenever we have a log function in this case the natural log function we have to make sure th... Read More

Key Insights

• 😑 Logarithmic functions have restrictions on their domain, requiring the expression inside the logarithm to be greater than zero.
• 😑 When the expression contains a variable in the denominator, set up an inequality and use the number line to determine the valid values for the variable.
• 😥 Check for critical points, such as values that make the denominator zero, and test values on either side of these points to find the valid intervals for the variable.

Questions & Answers

Q: How do you find the domain of a logarithmic function?

To find the domain of a logarithmic function, you need to ensure that the expression inside the logarithm is greater than zero. This can be done by setting up an inequality and solving for the variable.

Q: What is the role of the number line in finding the domain of logarithmic functions?

The number line is used to determine the valid values for the variable in the inequality. By testing values less than and greater than the critical points, you can identify the regions that satisfy the inequality and shade them to represent the domain.

Q: Why do we need to check for values that make the denominator zero?

Values that make the denominator zero will result in undefined fractions, which are not valid solutions. It is important to exclude these values from the domain of the logarithmic function.

Q: Can you explain the process of finding the domain with an example?

Sure! Let's say we have the function f(x) = Ln(1 / x - 5). To find the domain, we set up the inequality (1 / x - 5) > 0. Using a number line, we test values like 3 and 6 to check if they satisfy the inequality. The valid values are those that make the inequality true.

Summary & Key Takeaways

• To find the domain of a logarithmic function, ensure that the expression inside the logarithm is greater than zero.

• If the expression contains a variable in the denominator, set up an inequality and use a number line to find the valid values for the variable.

• Check for any values that make the denominator zero, as these will result in undefined fractions.

• Use the number line to test values less than and greater than the critical points, and shade the regions that satisfy the inequality to determine the domain.