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..)
