Тренажёр № 6 Вычислить. 1. lg 100 + lg 1000, 2. lg 0,1 + 2 lg 1000, 3. 3 lg 0,01 + 7/lg 0,1, 4. lg lg10, 5. 5 lg 1000- 7lg100, 6. lg 1 · lg 109, 7. (lg 0,001 + lg 100)2, 8. 8/lg100- 18/lg 0,01, 9. lg √100 : lg ³√1000, 10. √lg 10000 + 5 lg 10.

1. lg 100 + lg 1000 = 2 + 3 = 5

2. lg 0,1 + 2 lg 1000 = -1 + 2 \(\cdot\) 3 = -1 + 6 = 5

3. 3 lg 0,01 + 7/lg 0,1 = 3 \(\cdot\) (-2) + 7/(-1) = -6 - 7 = -13

4. lg lg 10 = lg 1 = 0

5. 5 lg 1000 - 7 lg 100 = 5 \(\cdot\) 3 - 7 \(\cdot\) 2 = 15 - 14 = 1

6. lg 1 \(\cdot\) lg 109 = 0 \(\cdot\) lg 109 = 0

7. (lg 0,001 + lg 100)² = (-3 + 2)² = (-1)² = 1

8. 8/lg 100 - 18/lg 0,01 = 8/2 - 18/(-2) = 4 + 9 = 13

9. lg √100 : lg ³√1000 = lg 10 : lg 10 = 1 : 1 = 1

10. √lg 10000 + 5 lg 10 = √4 + 5 \(\cdot\) 1 = 2 + 5 = 7

Ответ: 1) 5, 2) 5, 3) -13, 4) 0, 5) 1, 6) 0, 7) 1, 8) 13, 9) 1, 10) 7