conditia de existenta a logaritmului
3x-2>0 x>2/3 log[2]x=log in baza 2 din x
prelucrezi membrul drept
log[8](3x-2)=log[2³](3x-2)
Aplici proprietate logaritmilor
log[a^n] y^n=log[a]y si obtii
log[2³](3x-2)=log[2]∛(3x-2) =>
log[2]x=log[2]∛(3x-2). Delogaritmezi
x=∛(3x-2)
x³=3x-2
x³-3x+2=0
(x³-x)-2(x-1)=0
x*(x-1)*(x+1)-2(x-1)=0
(x-1)*(x²+x-2)=0
x1=1,
x2=-2 nu se accepta
x3=1
=>
x=1 solutie
