cours 10 LOGARITHME

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cours 10

LOGARITHME

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Propriétés des exposants.

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Soient

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Soient et

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1.

Soient et

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1.

2.

Soient et

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1.

2.

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Soient et

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Soient et

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Soient et

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1.

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Soient et

5.

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Si l’addition est faire des bond de

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et que la multiplication est faire des bond de

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et que la multiplication est faire des bond de et bien, l’exponentiation est faire des bond de

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Logarithme

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Logarithme

On définit comme l’inverse de l’exposant.

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Logarithme

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Exemple

Logarithme

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Exemple

Logarithme

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Exemple

Logarithme

car

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Exemple

Logarithme

car

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Exemple

Logarithme

car

Notation:

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Exemple

Logarithme

car

Notation:

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Exemple

Logarithme

car

Notation:

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Exemple

Logarithme

car

Notation:

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Propriétés des logarithmes

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Propriétés des logarithmes 1.

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Justification:

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2.

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Exemple

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Justification:

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Exemple

log₂(4 ⇥ 8)

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Justification:

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Exemple

log₂(4 ⇥ 8) = log₂ 4 + log₂ 8

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Justification:

3.

Exemple

log₂(4 ⇥ 8) = log₂ 4 + log₂ 8 = 2 + 3

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Justification:

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Exemple

log₂(4 ⇥ 8) = log₂ 4 + log₂ 8 = 2 + 3 = 5

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4.

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Exemple

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Justification:

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Exemple

log₂(8³)

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Justification:

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Exemple

log₂(8³) = 3 log₂(8)

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Justification:

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Exemple

log₂(8³) = 3 log₂(8) = 3 ⇥ 3

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Justification:

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Exemple

log₂(8³) = 3 log₂(8) = 3 ⇥ 3 = 9

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Remarque:

Formule de changement

de base

Justification:

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Remarque:

de base

Justification:

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log₈ 32

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Remarque:

de base

Justification:

5.

log₈ 32 = log₂ 32 log₂ 8

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Remarque:

de base

Justification:

5.

log₈ 32 = log₂ 32

log₂ 8 = 5 3

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Faites les exercices suivants

#2.1

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Faites les exercices suivants

#2.2 à 2.4

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Isoler une variable d’une équation contenant des log ou des puissances

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Exemple

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Exemple

2^3x+1 = 256

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Exemple

2^3x+1 = 256

log₂ 2^3x+1 = log₂ 256

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Exemple

2^3x+1 = 256

log₂ 2^3x+1 = log₂ 256 (3x + 1) log₂ 2 = 8

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Exemple

2^3x+1 = 256

log₂ 2^3x+1 = log₂ 256 (3x + 1) log₂ 2 = 8

3x + 1 = 8

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Exemple

2^3x+1 = 256

log₂ 2^3x+1 = log₂ 256

(3x + 1) log₂ 2 = 8 3x + 1 = 8

3x = 7

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Exemple

2^3x+1 = 256

log₂ 2^3x+1 = log₂ 256

(3x + 1) log₂ 2 = 8

3x + 1 = 8 3x = 7 x = 7

3

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Exemple

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Exemple

log₂(2x 5) = 5

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Exemple

log₂(2x 5) = 5 2^log²^(2x ⁵⁾ = 2⁵

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Exemple

log₂(2x 5) = 5 2^log²^(2x ⁵⁾ = 2⁵

2x 5 = 32

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Exemple

log₂(2x 5) = 5 2^log²^(2x ⁵⁾ = 2⁵

2x 5 = 32 2x = 37

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Exemple

log₂(2x 5) = 5 2^log²^(2x ⁵⁾ = 2⁵

2x 5 = 32 2x = 37

x = 37 2

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Faites les exercices suivants

# 2.5