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=2\sqrt {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" alt="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=2\sqrt {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" align="absmiddle" class="latex-formula">
ответ: 21