3.3 Logs and Their Graphs.notebook

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October 25, 2017

Feb 14­6:15 PM

3.3 Logarithmic Functions and Their Graphs Name: ___________________

Objective: Students will be able to convert equations betweenlogarithmic form and exponential form, evaluate common andnatural logarithms and graph them.

What in the world is a logarithm?

Logarithms are _____________.

Let b and y be positive numbers with b≠1. The logarithm of y with base b is denoted logby=x and is defined as follows:

logby=x if and only if bx=y

In words: logby=x is read "log base b of y".

Common log: log10x=logx Natural log: logex=lnx

Feb 14­6:26 PM

Examples: Rewrite in exponential form.

1.) log28=3 2.) log41=0

3.) log1212=1 4.) log2¼=-2

Examples: Rewrite in logarithmic form.

1.) 32=9 2.) 5-2=1/25

3.) (½)-3=8 4.) 40=1

Examples: Evaluate the logarithms.

1.) log525 2.) log381

3.3 Logs and Their Graphs.notebook

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October 25, 2017

Feb 14­6:29 PM

3.) log100 4.) log1/327 5.) lne4

6.) log91 7.) log√10 8.) log4(1/64)

Inverse Functions: The logarithmic function y = logbx and the exponential function y = bx are inverses. This means: logbbx=x and blog

bx=x.

Examples: Simplify.1.) 4log

4x 2.) log33x 3.) log5125x 4.) elnπ

Oct 25­7:56 AM

3.3 Logs and Their Graphs.notebook

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October 25, 2017

Oct 10­6:22 PM

Let's talk about log(-10)...

Examples Use a calculator to evaluate the expression, if it is defined.

1.) log(.908) 2.) log(-5.14) 3.) ln7

Examples Solve.1.) log3x = 2 2.) logx = -4

Oct 10­6:27 PM

Recall this wonderful function: f(x) = lnx

Domain:

Range:

Continuity:

Increasing/decreasing behavior:

Symmetry:

Boundedness:

Extrema:

H.A.

V.A.

End behavior:

3.3 Logs and Their Graphs.notebook

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October 25, 2017

Feb 14­6:41 PM

Examples: Graph. State the domain, range and V.A.1.) f(x) = -ln(x+2) 2.) f(x) = 2ln(-x) + 3

Feb 21­9:46 AM

3.) g(x) = log2x 4.) f(x) = log2(x -2)

3.3 Logs and Their Graphs.notebook

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October 25, 2017

Oct 10­6:34 PM

So...what are logarithms good for, anyways???

The level of sound intensity in decibels (dB) is β=10log(I/I0), where β is the number of decibels, I is the sound intensity in W/m2, and I0 = 10-12 W/m2 is the threshold of human hearing (thequietest audible sound intensity).

Example: A subway train has a sound intensity of 10-2 W/m2.How loud is the train?

Assignment: Pages 308-309: 1-35 odd, 37-40, 41, 49, 56, 59, 60

Oct 25­7:00 AM

Two Truths and One Lie

1.)  log100 = 2

2.)  log(1/100) = ‐2

3.)  log2 = 100

3.3 Logs and Their Graphs.notebook

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October 25, 2017

Oct 25­7:05 AM

Two Truths and One Lie

1.)  log28 = 3

2.)  log1/82 = ‐3

3.)  log82 = 1/3

Oct 25­7:03 AM

Two Truths and One Lie

1.)  The domain of f(x) = log(x ‐ 2) is (‐2,∞).

2.)  The domain of g(x) = log(2 ‐ x) is (‐∞, 2).

3.)  The domain of h(x) = log(x + 2) is (‐2,∞).

3.3 Logs and Their Graphs.notebook

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October 25, 2017

Oct 25­7:07 AM

Two Truths and One Lie

1.)  The range of f(x) = lnx is the same as the domain of g(x) = ex.

2.)  An exponential function can have a V.A.

3.)  A logarithmic function will have exactly one V.A.

Oct 25­7:10 AM

Two Truths and One Lie

1.)  logab = c can be rewritten as ac = b.

2.)  logba = c can be rewritten as bc = a.

3.)  logab = c can be rewritten as ab = c.