Question

Rezolvați în mulţimea numerelor reale ecuația ㏒₂ ײ-4×+12=㏒₃ 27

Answer 1

$log_2(x^2-4x+12)=log_327~~~~~~~~~~C.E.~~x^2-4x+12 > 0\\\\log_2(x^2-4x+12)=log_33^3\\\\log_2(x^2-4x+12)=3log_33\\\\log_2(x^2-4x+12)=3\\\\log_2(x^2-4x+12)=log_22^3\\\\x^2-4x+12=8\Rightarrow x^2-4x+12-8=0\Rightarrow x^2-4x+4=0\\\\a=1,~ b=-4,~c=4\\\\\Delta=b^2-4ac=(-4)^2-4\cdot1\cdot4=16-16=0\\\\\Delta=0\Rightarrow x_1=x_2=-\dfrac{b}{2a} =-\dfrac{-4}{2\cdot1} =2\\\\Solutia:~x=2$