Question

log_{2} x +log_{2} (x-1) = log_{2} 12

Answer 1

conditia de existent a logaritmilor x>0, x-1>0, x>1

log₂x(x-1)=log₂12
x(x-1)=12. x²-x-12=0, delta=(-1)²-4x(1)x(-12)=1+48=49, raddelta=7
x₁=-(-1)+7/2=8/2=4 verifica cond de existenta a logaritmilor
x₂=-(-1)-7/2=-6/2=-3<0 nu verifica cond de existent a logaritmilor