Question

log3(x-1)+log3(x+1)=1

Answer 1

DVA:sistem x-1>0 si x+1>0 Rezulta x>1 si x>-1 DVA: x>1; log3(x-1)+log3(x-1)=log3 3 Log3(x-1)(x+1)=log3 3 (X-1)(x+1)=3 Xpatrat-1=3 Xpartat=4 X=2 apartine DVA X=-2 nu apartine DVA. Deci X= 2

Answer 2

cond.de existenta pt.log:x-1>0⇒x>1 si x+1>0⇒x>-1⇒x∈(1,+∞)
log₃(x-1)+log₃(x+1)=log₃3
log₃(x-1)(x+1)=log₃3
(x-1)(x+1)=3
x²-1=3
x²=4 cu solutiile:x₁=-2∉(1,+∞) si x₂=2∈(1,+∞)⇒x=2 este solutie a ecuatiei