Lesson 3 Summary

 

In this lesson you explored the concept of logarithms. The inverse of an exponential function, y = cx, c > 0, c ≠ 1, is a logarithmic function, y = logc x, c > 0, c ≠ 1. A logarithm of a number is the exponent by which a given base must be raised to produce that number. You can change between exponential and logarithmic forms.

 

Exponential Form	Logarithmic Form
x = cy	y = logc x

 

The logarithmic function is the reflection of the exponential function in the line y = x. The characteristics of the logarithmic function y = logc x, c > 0, c ≠ 1 are as follows:

• The domain is {x|x > 0, x ∈ R}.
• The range is {y|y ∈ R}.
• The x-intercept is 1.
• The vertical asymptote is x = 0, or the y-axis.

In the next lesson you will explore the graphs of different logarithmic functions.