142. Вычислить: 1) \(4\log_{1/2}3-\frac23\log_{1/2}27-2\log_{1/2}6\); 2) \(\frac23\lg 0,001+\lg\sqrt[3]{1000}-\frac35\lg\sqrt{10000}\).

1. Используем \(\log_{1/2}27=3\log_{1/2}3\):
   \(4\log_{1/2}3-\frac23\cdot3\log_{1/2}3-2\log_{1/2}6=2\log_{1/2}3-2\log_{1/2}6\).
   Тогда получаем \(2\log_{1/2}(\frac36)=2\log_{1/2}(\frac12)=2\).
2. \(\lg0,001=-3\), \(\lg\sqrt[3]{1000}=\lg10=1\), \(\lg\sqrt{10000}=\lg100=2\).
   \(\frac23(-3)+1-\frac35(2)=-2+1-\frac65=-\frac{11}{5}=-2,2\).

Ответ: 1) 2; 2) −2,2.