Question

Ребят, помогите пожалуйста. Завтра нужно сдавать, а я решил только 1 :c
Желательно в письменной форме.

Answer 1

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