4.4 – Evaluate Logarithms and Graph Logarithmic

FunctionsGPS: MM3A2c, MM3A2e, MM3A2f

GPS MM3A2c – Define logarithmic functions as

inverses of exponential functions. MM3A2f – Graph functions as transformations

of f(x) = ax, f(x) = logax, f(x) = ex, f(x) = ln x. MM3A2e – Investigate and explain

characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Let b and y be positive numbers with b≠ 1. The logarithm of y with base b is denoted by and is defined as follows: = x if and only if

A common logarithm is a logarithm with base 10, denoted by log.

A natural logarithm is a logarithm with base e, denoted by ln.

A logarithmic function is a function of the form .

By definition of a logarithm, it follows that the logarithmic function is the inverse of the exponential function .

Vocabulary

Logarithmic Form Exponential Form

Example 1: Rewrite logarithmic equations (Page 145)

Evaluate the logarithm.

Example 2: Evaluate logarithms

b.) c) d)

Try page 145, 1-8

Guided Practice

What are these?

Before we answer that, what is a function? ◦ Think maps◦ How would we solve the following functions?

What are Inverses?

Domain Range

2

3

1) Switch the x and y2) Solve for y 3) How do we get rid of

different things like logs or natural logs?

4) Denote by using thefollowing:

Steps to finding the inverse of a function

• Logs are “undone” by exponents – and vice versa

• Natural logs (ln) are undone by e – or vice versa

Example

Find the inverse of the function.a) From the definition of logarithm, the

inverse of is

Find inverse function (Page 146)

Original function

Switch x and y

Write in exponential form.

Solve for y.

*The inverse is when you solve for y*

Graph State the domain and range.Same rules apply

Translate a logarithmic graph