Question

Rezolvati inecuatia:
2ln²x+1<3lnx, x∈(o,infinit)

Answer 1

notam ln x=y si rezolvam ca o inecuatie de gradul 2
2y²+1<3y
2y²-3y+1<0
radacinile sunt y1=2 si y1=1
y∈(1,2)
dar y=lnx
ln x=1⇒ln x= ln e⇒x=e deoarece e=2,71⇒x=2,71
ln x=2⇒conform formulei
ln x=ln e²
x=e²=7,35
x∈(e,e²)