Warm up!

.

10 2x

Solve for x

And before we get to the learnin’, any

questions from your homework?

The Wørd

Section 3.2Logarithmic

Functions and Their Graphs

So the frosh are 3-4.

Exponentiating

10xy

How do we get the x out of the exponent?

How do we solve for x?

Logarithmic Functions

It is read “y equals log base b of x.”

log yby x iff x b

Logs and exponential functions are freaking inverses!!!!!!!!

Which ain’t too bad.

Convert the log equation to an exponential equation and vice

versa.log 100 2

3log 27 3

I am 21-20 as a

coach…

Convert the log equation to an exponential equation and vice

versa.4

1log 1

4

35 125

…and now I’m hoping to be 23-

20.

Convert the log equation to an exponential equation and vice

versa.46 4096

3 17

343

Still not a great

record…

Evaluate the log without a calculator!

3log 9

2log 32

4log 2

…for me at least…

Evaluate the log without a calculator!

7

1log

49

5

1log

125

log 0

…but we’ve got some great kiddos playin’

ball.

Evaluate the log without a calculator!ln e

2ln e

ln 6e

If you’re not watching games at

all levels…

Props of Logarithms

log 1b

logb b

log

log

b

xb

x

b

and

b

…you’re missing

out.

Find the inverse of the given function.( ) 2xf x 4( ) log (2 )f x x

The frosh have 2 shutouts already…

Find the inverse of the given function.( ) 3 1xf x 6( ) log ( 1) 1f x x

…and they delivered some crushing hits.

2( ) log ( 3) 3f x x

-10 -5 5 10

10

8

6

4

2

-2

-4

-6

-8

-10

JV has some great talent too.

3( ) 2 log ( 1) 1f x x

-10 -5 5 10

10

8

6

4

2

-2

-4

-6

-8

-10

They’ve got blistering

speed and a stifling D.

1( ) ln ( 2) 3

2f x x

-10 -5 5 10

10

8

6

4

2

-2

-4

-6

-8

-10

And have you seen Robertó

Müdd?

The relationship between the number of decibels, β, and the

intensity of a sound, I, in w/m2 is given by:

1210log

10

I

a) Determine the # of decibels of a sound with intensity of 1 w/m2.

The relationship between the number of decibels, β, and the

intensity of a sound, I, in w/m2 is given by:

1210log

10

I

b) Determine the # of decibels of a sound with intensity of 10-2 w/m2.

The relationship between the number of decibels, β, and the

intensity of a sound, I, in w/m2 is given by:

1210log

10

I

c) The intensity of the sound in part a is 100 times greater than that of part b. Is the # of decibels 100 times greater?

Mr. Wu invests $5,000, the yearly maximum, in his Roth IRA. If it

usually gains 7% in interest a year, how long will it take to double in

value if it’s compounded continuously? rtA Pe

3.2 from the dern packet!And your homework!