Question

0,1 lg^4*x-lg^2x+0,9=0

Answer 1

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Answer 2

$0.1lg^4 x-lg^2 x+0.9=0;\\x>0;\\lg^2 x=t geq 0;\\0.1t^2-t+0.9=0;\\D=(-1)^2-4*0.1*0.9=1-0.36=0.64=0.8^2;\\t_1=frac{1-0.8}{2*0.1}=1;\\t_2=frac{1+0.8}{2*0.1}=9;\\lg^2 x=1=1^2;\\lg x=1;x_1=10^1;\\lg x=-1;x_2=10^{-1}=0.1;\\lg^2 x=9=3^2;\\lg x=3;x_3=10^3=1000;\\lg x=-3;x_4=10^{-3}=0.001$

ответ: 0.001;0.1;10;1000