Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown...

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Slide: 1 2.4 LOGARITHMS

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Slide: 3 The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 How can we calculate this? log = = log = = log = = Logarithm and its Relation to Exponents

Transcript of Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown...

Page 1: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 1

2.4 LOGARITHMS

Page 2: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 2

?

The use of logarithms is a fast method of finding an unknown exponent.

Section 7.4

Base Exponent

9 = 81?

3 = 27?2 = 16

Logarithm and its Relation to Exponents

Page 3: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 3

The use of logarithms is a fast method of finding an unknown exponent.

Section 7.4

How can we calculate this?

log 819

= log 27

3=

log 1007

=

Logarithm and its Relation to Exponents

Page 4: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 4

The logarithm of a number is the exponent by which a fixed number , the base, has to be raised to produce that number.

Section 7.4

ax = yBase

Exponent

Number

log

ya x= Base Number

Logarithm(Exponent)

Exponential form

Logarithmic form

Logarithm and its Relation to Exponents

Page 5: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 5

The logarithm of a number is the exponent by which a fixed number , the base, has to be raised to produce that number.

Section 7.4

43 = 64

54 = 625

Logarithm and its Relation to Exponents

Page 6: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 6

Most calculators can only solve for two special kinds of logarithms,the Common Logarithm (log) and the Natural Logarithm (ln).

Section 7.4

102 = 100

Common Logarithms and Natural Logarithms

Page 7: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 7

Most calculators can only solve for two special kinds of logarithms,the Common Logarithm (log) and the Natural Logarithm (ln).

Section 7.4

log 1 = 0log 10 = 1

log 100 = 2log 1000 = 3

Common Logarithms and Natural Logarithms

Page 8: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 8

Business calculators can only solve for the Natural Logarithm (ln), pronounced “lawn”. ln is to the base e, which is a special number.

Section 7.4

Natural logarithm

button

Common Logarithms and Natural Logarithms

Page 9: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 9

Business calculators can only solve for the Natural Logarithm (ln), pronounced “lawn”. ln is to the base e, which is a special number.

Section 7.4

e2 = 7.39 log 7.39e

= 2

ln7.39 = 2A logarithm to the base of e is called the natural logarithm.

It is abbreviated as “ln”, without writing the base.

Simply “ln” without a

base implies log .e

e = 2.718282

Common Logarithms and Natural Logarithms

Page 10: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 10

Business calculators can only solve for the Natural Logarithm (ln), pronounced “lawn”. ln is to the base e, which is a special number.

Section 7.4

ln 1 = 0ln e = 1

ln10 = 2.302585…ln1000 = 6.907755…

Common Logarithms and Natural Logarithms

Page 11: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 11

Common logarithms (log) and natural logarithms (ln) follow the same rules.

Section 7.4

Product Rule

ln AB = ln A + ln B

ln (2×3) =ln (15×25) =

Rules of Logarithms

Page 12: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 12

Common logarithms (log) and natural logarithms (ln) follow the same rules.

Section 7.4

Quotient Rule

= ln A − ln B ln AB ( )

=ln 32( )

=ln 2712( )

Rules of Logarithms

Page 13: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 13

Common logarithms (log) and natural logarithms (ln) follow the same rules.

Section 7.4

Power Rule

ln (A)n = nln A

ln (10)2 =

ln (67)4 =

Rules of Logarithms

Page 14: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 14

Common logarithms (log) and natural logarithms (ln) follow the same rules.

Section 7.4

0 as a power or 1 as logarithm

ln (A)0 = ln 1 = 0

ln (15)0 =

ln (32)0 =

Rules of Logarithms

Page 15: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 15

Solution

4n = 65,536

Solve for “n” in the following equation.

Page 16: Slide: 1 2.4 LOGARITHMS. Slide: 2 ? ? The use of logarithms is a fast method of finding an unknown exponent. Section 7.4 BaseExponent 9 = 81 ? ? 3 = 27.

Slide: 16

Solution

Solve for “n” in the equation 36(2)n = 147,456.