PRE-AP PRE-CALCULUSCHAPTER 3, SECTION 3

LOGARITHMIC FUNCTIONS AND THEIR GRAPHS

2013 - 2014

EXPONENTIAL FUNCTIONS & THEIR INVERSE

What did we do to find inverse functions?

With exponential function, they have a special inverse called _________________________.

Logarithmic functions with base b are denoted by or .

If with b > 0 but not equal to 1, then .

CHANGING BETWEEN LOGARITHMIC AND EXPONENTIAL FORM

If x > 0 and 0 < b ≠ 1, then

Example: write in exponential form

WRITE THE FOLLOWING LOGS IN EXPONENTIAL FORM

BASIC PROPERTIES OF LOGS

For 0 < b ≠ 1, x > 0, and any real number y,

because _____________

because _____________

because _____________

because ______________

EVALUATING LOGARITHMIC AND EXPONENTIAL EXPRESSIONS

COMMON LOGARITHMS

Logarithms with base 10 are called ___________________________.

Since base 10 logs are so common (our counting system, scientific notation, and metric system), the subscript 10 is often dropped from this log notation.

•

This common log is the inverse of the exponential function : _________________.

BASIC PROPERTIES OF COMMON LOGARITHMS

Let x and y be real numbers with x > 0

• because

• because

• because

• because

EVALUATING LOGS AND EXPONENTIAL EXPRESSIONS, BASE 10

EVALUATING COMMON LOGS WITH A CALCULATOR

SOLVING SIMPLE LOG EQUATIONS

Solve each equation by changing it to exponential form.

NATURAL LOGARITHMS – BASE

Logarithms with base are ___________________.

The abbreviation ______ is used to denote natural logarithms.

______ is the inverse function of _____.

BASIC PROPERTIES OF NATURAL LOGARITHMS

Let x and y be real numbers with x > 0.

• because _________

• because _________

• because ___________

• because ____________

EVALUATING LOGARITHMIC AND EXPONENTIAL EXPRESSIONS – BASE

EVALUATING NATURAL LOGARITHMS WITH A CALCULATOR

Use a calculator to evaluate the logarithmic expression, if it is defined, and check your result by evaluating the corresponding exponential expression.

GRAPH THE FUNCTION

[-2, 6] by [-3, 3]

Domain:

Range:

Continuity:

Increasing:

Symmetry:

Extrema:

Asymptotes:

End Behavior:

GRAPHS OF INVERSE FUNCTIONS

Graph a set of logarithmic equations that are inverses of each other in the window [-5, 5] by [-5, 5]

GRAPHS OF INVERSE FUNCTIONS

Graph a set of logarithmic equations that are inverses of each other in the window [-5, 5] by [-5, 5]

CH 3.3 HOMEWORK

Pg 308 – 309, #’s: 1 – 21 every other odd, 33, 53, 61, 65

Total problems: 10

Gray Book: 281 - 282