3.2 Logarithmic Functions and Their Graphs

3.2 Logarithmic Functions and Their Graphs

Integrated Math 3

Mr. Washington

January 20, 2020

Objectives

• Recognize and evaluate logarithmic functions with base a.

• Graph logarithmic functions.

• Recognize, evaluate, and graph natural logarithmic functions.

•  Use logarithmic functions to model and solve real-life problems.

Evaluating Logarithms

Use the definition of logarithmic function to evaluate each logarithm at the indicated value of x.

Fill in the Blank

 $f\left(x\right)=\ \log_{10}\ x\ ,\ x=\frac{1}{100}$  

Fill in the Blank

 $f\left(x\right)=\log_4\ x,\ x=2$  

Logarithmic Functions

The logarithmic function with base 10 is called the common logarithmic function. On most calculators, this function is denoted by the “log” key.

Evaluating Common Logarithms on a Calculator

Use a calculator to evaluate the function f (x) = log10 x at each value of x.

Using Properties of Logarithms

Solve for x

Multiple Choice

Simplify : $\log_5\ 5^x$   

• 5

• 1

• x

Multiple Choice

 $6^{\log_6\ 20}$  

Simplify:

• 6

• x

• 20

Graphs of Logarithmic Functions 

To sketch the graph y = loga x, you can use the fact that the graphs of inverse functions are reflections of each other in the line y = x.

Graph of

 $y=\log_a\ x,\ a>1$  

Evaluating the Natural Logarithmic Function

Use a calculator to evaluate the function f (x) = ln x for each value of x.

Fill in the Blank

 $\frac{\ln\ 1}{3}$  

Fill in the Blank

 $2\ \ln\ e$