Algèbre

Question 1

Logarithme:
log_b(x) = y
ou
b^y = x

log₂(8) = 3
&
3⁴ = 81
&
log₇(1) = 0

Answer 1

2³ = 8
&
log₃(81) = 4
&
7⁰ = 1

Question 2

Type de logarithme:
- Log Décimal
- Log Népérien (ln)
- Log Binaire (base 2)

Answer 2

Notation:
- log₁₀
- ln
- log₂

Question 3

Le logarithme d’un Produit/Quotient:
log_b(M×N) = log_bM + log_bN
log_b(M÷N) = log_bM - log_bN

log₁₂4 + log_b36
log₂320 - log₂5

Answer 3

= log₁₂(4 × 36)
= log₁₂(144)

= log₂(320/5)
= log₂64

Question 4

Logarithme d’une puissance:
log_bMⁿ = n × log_bM

log₇49² = ?

Logarithme fractionnaire:
log_1/bM = -log_bM

log_1/381 = ?

Answer 4

= 2 × log₇49
4³ = 64
= 4

= -log₃81
3⁴ = 81
= -4

Question 5

Changement de base:
log₁₆128 =

Answer 5

= log₂128 / log₂16
= 7 / 4