# 3.3 PROPERTIES OF LOGARITHMS - Utep

date post

09-Feb-2022Category

## Documents

view

0download

0

Embed Size (px)

### Transcript of 3.3 PROPERTIES OF LOGARITHMS - Utep

Slide 12

evaluate logarithmic expressions.

rewrite logarithmic expressions.

condense logarithmic expressions.

real-life problems.

a.

b.

Example 3 – Using Properties of Logarithms

Write each logarithm in terms of ln 2 and ln 3.

a. ln 6 b. ln

Solution:

= ln 2 + ln 3

= ln 2 – ln 33

Product Property

Power Property

Find the exact value of each expression without using a

calculator.

= log5 5 1 3 =

= 6 ln − 2 ln = 6 − 2 = 4

= ln 6

2 = ln 6−2 = ln 4 = 4 ln = 4

10

Expand each logarithmic expression.

a. log4 5x3y = log4 5 + log4 x 3 + log4 y

= log4 5 + 3 log4 x + log4 y

Product Property

Power Property

= log 1 2 + log + 1 3

= log 1 2 + 1 3

= log + 1 3

14

Continue…

= ln + 2 2

= 1

= log2 ( + 1) 3

16

Application

17

Application

If the points are graphed and fall on a line, then you can

determine that the x- and y-values are related by the

equation

where m is the slope of the line.

18

19

Y= 3

2 X, where Y = ln x and X = ln x

ln = 3

2 ln

evaluate logarithmic expressions.

rewrite logarithmic expressions.

condense logarithmic expressions.

real-life problems.

a.

b.

Example 3 – Using Properties of Logarithms

Write each logarithm in terms of ln 2 and ln 3.

a. ln 6 b. ln

Solution:

= ln 2 + ln 3

= ln 2 – ln 33

Product Property

Power Property

Find the exact value of each expression without using a

calculator.

= log5 5 1 3 =

= 6 ln − 2 ln = 6 − 2 = 4

= ln 6

2 = ln 6−2 = ln 4 = 4 ln = 4

10

Expand each logarithmic expression.

a. log4 5x3y = log4 5 + log4 x 3 + log4 y

= log4 5 + 3 log4 x + log4 y

Product Property

Power Property

= log 1 2 + log + 1 3

= log 1 2 + 1 3

= log + 1 3

14

Continue…

= ln + 2 2

= 1

= log2 ( + 1) 3

16

Application

17

Application

If the points are graphed and fall on a line, then you can

determine that the x- and y-values are related by the

equation

where m is the slope of the line.

18

19

Y= 3

2 X, where Y = ln x and X = ln x

ln = 3

2 ln