Question

lg(3x-2)-2=1/2lg(x+2)-lg50

Answer 1

$lg (3x-2)-2=frac{1}{2}lg (x+2)-lg 50;\ 3x-2>0; x+2>0;\ x>frac{2}{3}; x>-2;\ x>frac{2}{3};\ lg (3x-2)-lg 10^2= lg sqrt {x+2}-lg 50;\ lg frac {3x-2}{100}= lg frac{sqrt {x+2}}{50};\ frac {3x-2}{100}=frac{sqrt {x+2}}{50};\ 3x-2=2sqrt {x+2};\ 9x^2-12x+4=4(x+2);\ 9x^2-12x+4=4x+8;\ 9x^2-16x-4=0;\ D=(-16)^2-4*9*(-4)=400=20^2;\ x_1=frac{-(-16)-20}{2*9}<0<frac{2}{3};\ x_2=frac{-(-16)+20}{2*9}=2$

ответ: 21