# 1.2 The Natural Logarithmic Function

In this lesson, you will learn about natural logarithmic function.

### Lesson Objectives

• Recognize that the natural logarithm is a function defined by an integral.
• Derive the familiar precalculus properties of logarithms using the integral definition and calculus properties and procedures.
• Evaluate derivatives and integrals involving the natural logarithmic function.
• Evaluate derivatives involving logarithmic functions with other bases.
• Correctly use logarithmic differentiation to find derivatives of functions written as products and/or quotients of simpler functions.
• Model and solve applied problems involving logarithmic functions.

### Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

1. YouTube video: Pre-calculus Introduction to Logarithms
2. YouTube videos: Pre-calculus Introduction to Logarithm Properties
Part 1:

Part 2:

3. YouTube video: Calculus definition of the Natural Logarithm as an Integral function
4. The Natural Logarithm
5. Brightstorm video: Logarithmic Functions
6. YouTube videos: Properties of Logarithms
Part 1:

Part 2:

7. YouTube video: Derivatives of Logarithmic Functions

More examples:

8. YouTube videos: Derivatives of Natural Logarithms
– Part 6:3b – Additional Examples
– Part 6.3c – Derivatives of Base b Logarithms
9. YouTube videos: Logarithmic Differentiation
Example 2:

Example 3:

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

1. Natural Logarithm
2. Logarithmic Differentiation
3. Logarithmic Differentiation  (with examples and solutions)

### Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

1. Logarithm Functions
2. Logarithm Functions
3. Logarithmic Differentiation (skip the problems with exponential functions for now)
4. Logarithmic Differentiation (skip problem 5 for now)
5. Logarithmic Differentiation (problems with solutions)