Evaluate Logarithms and Graph Logarithmic Functions

Lesson 7.4 Part IAlgebra II

Agenda

1. Return Quizzes2. AMC and CAHSEE3. Review Homework4. Lesson Evaluate Logarithms (and Graph

Logarithmic Functions) Part I.5. Homework: Lesson 7.4a

Evaluate Logarithms and Graph Logarithmic Functions

Close the books! Put them on the shelf!

Evaluate Logarithms and Graph Logarithmic Functions

Can you figure out the relationship?

What do you think a logarithm is?

Evaluate Logarithms and Graph Logarithmic Functions

Definition of a Logarithm with Base b:

1. In your words

Evaluate Logarithms and Graph Logarithmic Functions

In the books words:

Definition of Logarithm with Base bLet b and y be positive numbers with The logarithm of y with base b is denoted by and is defined as follows:

The expression is read lobe base b of y.

Evaluate Logarithms and Graph Logarithmic Functions

Practice writing in exponential form from logarithmic expressions:

Evaluate Logarithms and Graph Logarithmic Functions

Now we need to evaluate logarithms:Find –

Evaluate Logarithms and Graph Logarithmic Functions

Special Bases:

Often two special bases are used… one is base 10 and log is called the common log. When there is no designation of base we are using 10. So

Evaluate Logarithms and Graph Logarithmic Functions

The other special base is e, the natural number. For this case we use the abbreviation ln for natural log…

Often we will need either a log table or a calculator to work these out.

Evaluate Logarithms and Graph Logarithmic Functions

Evaluate the following using a calculator, then check your answer by putting it into exponential form and checking it.