6.5 Applications of Common Logarithms Objectives: Define and use the common logarithmic function to solve exponential and logarithmic equations. Evaluate.

6.5 Applications of Common Logarithms

Objectives: Define and use the common logarithmic function to solve exponential and logarithmic equations.Evaluate logarithmic expressions by using the change-of-base formula.

Standard: 2.8.11.N. Solve exponential equations.

Warm Up:

1.51 0.25 -2.30

310

.001

v

v

2

2 2

49

7

7

v

v

v

2

2 1

16 4

(4 ) 4

4 4

2 1

1

2

v

v

v

v

v

x 10 100 1000 10,000 100,000 …

y = log x …

The base 10 logarithm is called the common logarithm.

In general, logarithmic functions are used to assign large values in the domain to small values in the range.

1 2 3 4 5

Recall from lesson 2.7 that the graph of y = a*f(x) is the graph of y = f(x) stretched by a factor of a. Therefore the graph of y = 10 log x is the graph of y = log x stretched by a factor of 10.

0

0

30010log

IR

I

10log300R

25 decibelsR

0

10logI

RI

0

70 10logI

I

0

10log70

10 10

I

I

0

7 logI

I

7

0

10I

I

7010 I I

The running vacuum cleaner is about

710 , or 10,000,000

times as loud as the threshold of hearing.

log8 log 792x

log8 log 792x

log 792 =

log8x

3.21x

You can use the change-of-base formula to change a logarithmic expression of any base to base 10 so that you can use the LOG key on your calculator.

8

log36log 36

log8

p. 389 #10-16 even

p. 390: #28-34 Even

Homework:

Practice 6.5

Chapter 6 Test FRIDAY!