Решите неравенства: [latex]lg( x^{2} -x+8) extgreater 1[/latex] [latex]lg2x extless lg(x+1)[/latex]

[latex]1); lg(x^2-x+8) extgreater 1; ,\\ODZ:; x^2-x+8 extgreater 0; ;D<0o ; xin R\\x^2-x+8 extgreater 10\\x^2-x-2 extgreater 0\\(x+1)(x-2) extgreater 0\\+++(-1)---(2)+++\\xin (-infty,-1)U(2,+infty)[/latex][latex]2); lg2x extless lg(x+1); ,; ; ODZ:; left { {{2x extgreater 0} atop {x+1 extgreater 0}} ight. ; , left { {{x extgreater 0} atop {x extgreater -1}} ight. ; o ; x extgreater 0\\2x extless x+1\\x extless 1\\0 extless x extless 1\\xin (0,1)[/latex]