How To Find The Domain of Logarithmic Functions | Precalculus

TL;DR

Learn how to find the domain of logarithmic functions by setting the inside part greater than zero.

Transcript

in this video we're going to talk about how to find the domain of a logarithmic function so let's start with the function log base 2 of x if you were to graph this function it would look something like this it has a vertical asymptote of x equals zero and the x-intercept is at one notice that this graph it never touches the y-axis nor is it on the ... Read More

Key Insights

• 😫 The domain of a logarithmic function is determined by setting the inside part greater than zero.
• 😵 The graph of a logarithmic function never touches or crosses the y-axis, and the inside part must be a positive value.
• 🤗 Excluded values in the domain are denoted by open circles on a number line.

Questions & Answers

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

To find the domain, set the inside part of the logarithm greater than zero and solve for the variable. Any excluded values should be denoted with open circles on a number line.

Q: Can the domain of logarithmic functions include negative numbers?

No, the domain of logarithmic functions cannot include negative numbers, as the logarithm of a negative number is undefined.

Q: What happens if you plug in zero or a negative number into a logarithmic function?

Plugging in zero or a negative number into a logarithmic function will result in an error or undefined value, as the logarithm of zero or a negative number does not exist.

Q: How can the domain of logarithmic functions be represented using interval notation?

The domain can be written using interval notation, indicating the range of values that the variable can take. For example, (-5, infinity) would represent all values greater than -5.

Summary & Key Takeaways

• Logarithmic functions have restrictions on their inputs, called the domain, which must be greater than zero.

• To find the domain, set the inside part of the logarithm greater than zero and solve for the variable.

• The domain may have excluded values, represented by open circles on a number line, and can be written using interval notation.