Lg(x^4-x^2-3)=lg(x^4+3x-7)

[tex]\displaystyle\lg(x^4-x^2-3)=\lg(x^4+3x-7)\\\\\left \{ {{x^4-x^2-3=x^4+3x-7} \atop {x^4-x^2-3>0~~~~~~~~~~~}} \right.\\\\\\\left \{ {{x^2+3x-4=0} \atop {x^4-x^2-3>0}} \right. \\\\\\\left \{ {{(x-1)(x+4)=0} \atop {x^4-x^2-3>0}} \right.[/tex]

[tex]1)~x-1=0;~~~x = 1;~~~1^4-1^2-3=-3<0[/tex]   -  не подходит

[tex]2)~x+4=0;~~~x =-4\\~~~~~~~~~~(-4)^4-(-4)^2-3=256-16-3=237>0\\\\\boxed{\boldsymbol{x=-4}}[/tex]