Question

lg^6 x-9*lg^3 x+8=0 решите очень срочно надо!!!!

Answer 1

$lg^6 x-9cdotlg^3 x+8=0, \ x textgreater 0, \ lg^3 x=a, \ a^2-9a+8=0, \ a_1=1, a_2=8, \ \ lg^3 x=1, \ lg x=1, \ x=10, \ \ lg^3 x=2^3, \ lg x=2, \ x=100.$

Answer 2

$log^6x-9log^3x+8=0 \ logx=z;x textgreater 0 \ z^6-9z^3+8=0 \ z^3=t \ t^2-9t+8=0 \ Delta=(-9)^2-4*8=81-32=49 textgreater 0 \ t_1= frac{9-7}{2}=1;t_2= frac{9+7}{2}=8 \ z^3=1Rightarrow z=1 \ logx=1iff x=10^1iff x=10 \ logx=2 iff x=10^2=100 \ x_1=10;x_2=100$