Тренажёр № 8 Вычислить. 1. log62+ log6 18, 2. log3 81.27, 3. log2 32 . 128, 4. log2 5 + log2 1/40 5. log5 0,25 + logs 100, 6. 2 logo,2 25 0,008, 7. 10 log2 1/320 10, 8. log4 0,5 + log4 8, 9. 5 log12 36 + 5log124, 10. 10 log20160 + 10 log20 50.

1. log₆ 2 + log₆ 18 = log₆ (2 \(\cdot\) 18) = log₆ 36 = 2, так как 6² = 36

2. log₃ 81 \(\cdot\) 27 = log₃ (3⁴ \(\cdot\) 3³) = log₃ (3⁷) = 7, так как 3⁷ = 2187

3. log₂ 32 \(\cdot\) 128 = log₂ (2⁵ \(\cdot\) 2⁷) = log₂ (2¹²) = 12, так как 2¹² = 4096

4. log₂ 5 + log₂ (1/40) = log₂ (5 \(\cdot\) (1/40)) = log₂ (1/8) = -3, так как 2^-3 = 1/8

5. log₅ 0,25 + log₅ 100 = log₅ (0,25 \(\cdot\) 100) = log₅ 25 = 2, так как 5² = 25

6. 2 log_0.2 25 \(\cdot\) 0,008 = 2 log_0.2 (25 \(\cdot\) 0,008) = 2 log_0.2 (0,2) = 2 \(\cdot\) 1 = 2

7. 10 log₂ (1/320) \(\cdot\) 10 = 10 log₂ (10/320) = 10 log₂ (1/32) = 10 \(\cdot\) (-5) = -50, так как 2^-5 = 1/32

8. log₄ 0,5 + log₄ 8 = log₄ (0,5 \(\cdot\) 8) = log₄ 4 = 1, так как 4¹ = 4

9. 5 log₁₂ 36 + 5 log₁₂ 4 = 5 log₁₂ (36 \(\cdot\) 4) = 5 log₁₂ 144 = 5 \(\cdot\) 2 = 10, так как 12² = 144

10. 10 log₂₀ 160 + 10 log₂₀ 50 = 10 log₂₀ (160 \(\cdot\) 50) = 10 log₂₀ 8000 = 10 \(\cdot\) 3 = 30, так как 20³ = 8000

Ответ: 1) 2, 2) 7, 3) 12, 4) -3, 5) 2, 6) 2, 7) -50, 8) 1, 9) 10, 10) 30