Bonjour j’ai besoin d’aide svp pour ce devoir de maths je n’ai fait aucun chapitre dessus et je ne comprends pas.. Si quelqu’un pourrait m’aider svp merci

Bonjour,

Propriétés opératoires des logarithmes :

log(a x b) = log(a) + lob(b)

log(a/b) = log(a) - log(b)

log(aᵇ) = b x log(a)

Ex 3

X = log(3/5) + log(10/9)

= log(3) - log(5) + log(10) - log(9)

= log(3) - log(5) + log(2x5) - log(3x3)

= log(3) - log(5) + log(2) + log(5) - 2log(3)

= log(2) - log(3)

= log(2/3)

Y = log(4/9) - log(7/3)

= log(2²) - log(3²) - log(7) + log(3)

= 2log(2) - 2log(3) - log(7) + log(3)

= 2log(2) - log(3) - log(7)

= 2log(2) - (log(3) + log(7))

= log(4) - log(3x7)

= log(4/21)

III)

(1,3)ˣ = 2

log((1,3)ˣ) = log(2)

xlog(1,3) = log(2)

x = log(2)/log(1,3)       (≈2,64...)

(2,5)ˣ = 0,1

log((2,5)ˣ) = log(0,1)

xlog(2,5) = log(0,1)

x = log(0,1)/log(2,5)

x = log(10⁻¹)/log(2,5)

x = -log(10)/log(2,5)

x = -1/log(2,5)   (≈ -2,51..)