Question

Am nevoie de mare ajutor , poate cineva sa ma ajute sa rezolv aceste ecuatii?!!

Answer 1

1. log₃(x²-1)=1
x²-1>0, x∈(-∞,-1)U(1,+∞)
log₃(x²-1)=log₃ 3, x²-1=3, x²-4=0, x=2, x=-2
2.log₅(x²+1)=1, x²+1>0
log₅(x²+1)=log₅ 5, x²+1=5, x²-4=0, x=-2, x=2
3. log√6(x²-5)=2, x²-5>0, x∈(-∞,-√5)U(√5, +∞)
log√6(x²-5)=2log√6√6, log√6(x²-5)=log√66, x²-5=6, x²-11=0, x=-√11, x=√11
4. log₂(x²-3x+10)=3, x²-3x+10>0, Δ<0
log₂(x²-3x+10)=log₂2³
x²-3x+10=8, x²-3x+2=0, x=1, x=2
5.log₂(x²-3x+4)=log₂4, x²-3x+4>0, Δ<0
x²-3x+4=4, x²-3x=0, x(x-3)=0, x=0, x=3
6.log₅(x²-11x+43)=log₅5², x²-11x+43>0, Δ>0
x²-11x+43=25, x²-11x+18=0, x=2, x=9