1. Exercice 23
(a)
log(xy) = 3
log x = 1
y
xy = 103 = 1000 1
x
y
= 101 = 10 2
De la seconde équation on tire : x = 10y.
L’équation 1 devient :
(10y) · y = 1000
10y2 = 1000
y = 10
y2 = 100
y = −10

2. Exercice 23 (suite..)
x
• Si y = 10 → = 10 → x = 100
10
x
• Si y = −10 → = 10 → x = −100
−10
S = {(x = 100; y = 10); (x = −100; y = −10)}
(b)
log(x) + log(y) = 2
x + y = 25
log(xy) = 2
x + y = 25
xy = 102 = 100
x + y = 25

3. Exercice 23 (suite..)
x = 25 − y que l’on remplace dans la première équation :
(25 − y)y = 100
− y2 + 25y = 100
y = 20
y2 − 25y + 100 = 0
y=5
• Si y = 20 → x = 25 − 20 = 5
• Si y = 5 → x = 25 − 5 = 20
S = {(x = 5; y = 20); (x = 20; y = 5)}