[tex]27^x+3^x\cdot(\sqrt3)^x=756\Rightarrow 27^x+(3\sqrt3)^x=756 \Rightarrow [(\sqrt{27})^2]^x+(\sqrt27)^x=756\Rightarrow[/tex]
[tex][(\sqrt{27})^x]^2+(\sqrt27)^x-756 =0\\ \\ Not\breve am\ (\sqrt{27})^x=t,\ \ t>0,\ \ iar\ ecua\c{\it t}ia\ devine:\\ \\ t^2+t-756=0 \Rightarrow t^2+t-27-729=0\Rightarrow (t-27)+t^2-27^2=0\Rightarrow \\ \\ \Rightarrow (t-27)+(t-27)(t+27)=0\Rightarrow (t-27)(1+t+27)=0\Rightarrow \\ \\ (t-27)(t+28)=0\ \stackrel{t>0}{\Longrightarrow}\ t=27[/tex]
Revenim asupra notației :
[tex]\it t=27\Rightarrow (\sqrt{27})^x=27\Rightarrow (\sqrt{27})^x=(\sqrt{27})^2\Rightarrow x=2[/tex]
