bonjour
on sait que a² + b² = 7ab
a)
(a + b)² = a² + 2ab + b²= (a² + b²) + 2ab = 7ab + 2ab = 9ab
(a + b)² = 9ab
b)
log(a + b)² = 2log(a + b) (1)
log 9ab = log 9 + log a + log b
= log 3² + log a + log b
= 2log 3 + log a + log b (2)
(1) = (2)
2log(a + b) = 2log 3 + log a + log b (on divise les 2 membres par 2)
log(a + b) = 1/2( 2log 3 + log a + log b)
log(a + b) = log3 + (1/2) (loga + logb)
