Graphing logarithmic functions | Exponential and logarithmic functions | Algebra II | Khan Academy

TL;DR

This video explains how to graph a logarithmic function and discusses the relationship between exponential and logarithmic equations.

Transcript

We're asked to graph, y is equal to log base 5 of x. And just to remind us what this is saying, this is saying that y is equal to the power that I have to raise 5 to to get to x. Or if I were to write this logarithmic equation as an exponential equation, 5 is my base, y is the exponent that I have to raise my base to, and then x is what I get when ... Read More

Key Insights

• 🤨 Logarithmic functions with base 5 can be written as y = log base 5 of x, where y represents the power to which 5 is raised to get x.
• 🤨 Graphing a logarithmic function involves finding y-values by raising the base to the power of the chosen x-values.
• 💁 The relationship between exponential and logarithmic equations is that they express the same information in different forms.
• ✊ The domain of a logarithmic function is x > 0, as there are no powers that can be raised to 5 to get negative or zero values.
• 📫 As x approaches infinity, the graph of a logarithmic function gets closer to the x-axis but never touches it.

Questions & Answers

Q: How does graphing a logarithmic function differ from graphing an exponential function?

Graphing a logarithmic function involves finding the y-values by raising the base to the power of the chosen x-values, while graphing an exponential function involves finding the x-values by raising the base to the power of the chosen y-values.

Q: What is the domain of the logarithmic function y = log base 5 of x?

The domain of this logarithmic function is x > 0 because there are no powers that can be raised to 5 to get negative or zero values.

Q: How does the graph of a logarithmic function behave as x approaches infinity?

As x gets larger and larger, the graph of a logarithmic function gets closer and closer to the x-axis, but it never touches it.

Q: What happens to the graph of a logarithmic function as x approaches zero?

As x gets smaller and approaches zero, the graph of a logarithmic function becomes steeper and approaches negative infinity in the y-direction.

Summary & Key Takeaways

• The video explains that a logarithmic function with base 5 can be written as y = log base 5 of x, which means y is the power to which 5 is raised to get x.

• By converting the logarithmic equation into an exponential equation (5^y = x), it becomes clear that logarithmic and exponential equations convey the same information.

• The video demonstrates how to create a table of values using nice, round numbers for x and calculate the corresponding y-values by raising 5 to the power of the chosen numbers.