Question

Прошу с объяснением.

Answer 1

$3\cdot \Big(1-\dfrac{1}{lg5}\Big)\Big(1-\dfrac{1}{lg2}\Big)=3\cdot \dfrac{lg5-1}{lg5}\cdot \dfrac{lg2-1}{lg2}=3\cdot \dfrac{lg5\cdot lg2-lg5-lg2+1}{lg5\cdot lg2}=\\\\\\=3\cdot \dfrac{lg5\cdot lg2-(lg5+lg2)+1}{lg5\cdot lg2}=\dfrac{3\cdot (lg5\cdot lg2-lg10+1)}{lg5\cdot lg2}=\\\\\\=\dfrac{3\cdot lg5\cdot lg2-1+1}{lg5\cdot lg2}=\dfrac{3\cdot lg5\cdot lg2}{lg5\cdot lg2}=3$

Answer 2

3*(1-(1/lg5))*(1-(1/lg2))=

3*(lg5-1)(lg2-1)/(lg2*lg5)=

3*(lg5*g2-lg5-lg2+1)/(lg2*lg5)=

3*(lg2*lg5-lg10+1)/(lg2*lg5)=3*(lg2*lg5)/(lg2*lg5)=3

Ответ 3