Ребят, помогите пожалуйста. Завтра нужно сдавать, а я решил только 1 :c Желательно в письменной форме.
Пожалуйста , с решением .
2. 16^(log₄ 3)= 4^(2log₄ 3) = 4^(log₄ 3²)= 3² =9 3. log₀.₅ 64 = log₁/₂ 2⁶ = log₁/₂ (1/2)⁻⁶ = -6 4. log₂ 16=log₂ 2⁴ =4 5. log₈ 512 * log₂ 32 = log₈ 8³ * log₂ 2⁵ = 3*5=15 6. log₁₂ 252 - log₁₂ 1.75 = log₁₂ (252/1.75)= log₁₂ 144 = log₁₂ 12² =2 7. log₅ 5 + log₀.₂₅ 64 = 1 + log₁/₄ 4³ = 1+log₁/₄ (1/4)⁻³ =1-3= -2 8. log₁.₈ 5 - log₁.₈ 9 = log₁.₈ (5/9)=log₉/₅ (9/5)⁻¹ = -1 9. log₀.₈ 3 * log₃ 1.25 = 1 * log₃ 1.25 = log₃ 1.25 = log₀.₈ 1.25 = log₃ 0.8 log₃ 0.8 = log₈/₁₀ (10/8)=log₈/₁₀ (8/10)⁻¹ = -1 10. log₉ 10 + log₁₁ 0.1 = log₁₁ 10 + log₁₁ 0.1 =log₁₁ (10*0.1)=log₁₁ 1 =0 log₉ 11 11. log₂ 5 * log₅ 8 = log₅ 8 = log₂ 8 = log₂ 2³ = 3 log₅ 2 12. log₂ 3.2 + log₂ 5=log₂ (3.2*5)=log₂ 16 = log₂ 2⁴= 4 13. (1-log₆ 54)(1-log₉ 54)=(log₆ 6 - log₆ 54)(log₉ 9 - log₉ 54)= = log₆ (6/54) * log₉ (9/54) = log₆ (1/9) * log₉ (1/6) = = log₉ (1/6) = - log₁/₉ (1/6) = log₁/₉ (1/6)⁻¹ = log₁/₉ 6 = 1 log₁/₉ 6 log₁/₉ 6 log₁/₉ 6 log₁/₉ 6 14. 100 log₆ ⁴√6 = 100 * (¹/₄) log₆ 6 = 25*1=25 15. log(⁵√12) 12 = 1/¹/₅ log₁₂ 12 = 5*1 =5 16. log₂ 48 = log₂ 48 = log₂ 48 = log₂ 48 = 1 3+log₂ 6 log₂ 2³ + log₂ 6 log₂ (8*6) log₂ 48 17. log₃ 14 = log₃ 14 = log₃ 14 = 1 = 2 log₉ 14 log₃² 14 ¹/₂ log₃ 14 ¹/₂ 18. log₆ 81 = log₉ 81 = log₉ 9² = 2 log₆ 9 19. 5^(log₂₅ 49) =5^(log₅² 7²) = 5^(²/₂ log₅ 7)= 5^(log₅ 7) = 7 20. log²√₈ 64 = log² (8^(¹/₂)) (64²)^(¹/₂) = log²₈ 64² = = log²₈ 8⁴ = 4² = 16 21. 9^(3log₉ 11)=9^(log₉ 11³) = 11³ = 1331 22. 4^(log₂ √3) = 2^(2log₂ √3)= 2^(log₂ (√3)²) = 2^(log₂ 3) = 3 23. log₄ log₉ 81 = log₄ log₉ 9² = log₄ 2 = log₂² 2 = ¹/₂ log₂ 2 = 1/2 24. 60 = 60 = 6 4^(log₄ 10) 10 25. log₁/₈ √8 = log₈⁻¹ 8^(¹/₂) = -¹/₂ log₈ 8 = -1/2 26. 4^(log₆ 72) = 4^(log₆ 72 - log₆ 2) = 4^(log₆ (72/2)) = 4^(log₆ 36) = 4^(log₆ 2) = 4² = 16 27. log₃ √5 = log₅ √5 = 1/2 log₃ 5 28. (5^(log₃ 7))^log₇ 3 = 5^(log₃ 7 * log₇ 3) = 5^(log₇ 3/log₇ 3)=5¹ =5
