Question

log in baza 3 din ( x^2-1) = 2 + log in baza 3 din ( x-1 )

Answer 1

DVA:x>1
$log_{3}( x^{2}-1)= log_{3}9+ log_{3}(x-1)$
[tex] log_{3}( x^{2} -1)= log_{3}9(x-1) [/tex]
$x^{2} -1=9(x-1)$
$x^{2} -9x+8=0$
Δ=81-32=49
$x_{1} = \frac{9-7}{2}=1$
$x_{2}= \frac{9+7}{2}=8$
Raspuns:{8}