2. Найдите значения: 1) log₅ 16 + log₅ 2; 2) log₃ 162 − log₃ 2; 3) log₃ 54 − log₃ 6; 4) log₄,₅ 4,5; 5) 8^(log₈ 12); 6) log₁₂ 144⁴; 7) log₁₉ 1; 8) log₃ 3; 9) log₃ 13,5 + log₃ 2; 10) log₂ 64¹¹.

1. log₅ 16 + log₅ 2 = log₅ 32.
2. log₃ 162 − log₃ 2 = log₃ 81 = 4.
3. log₃ 54 − log₃ 6 = log₃ 9 = 2.
4. log₄,₅ 4,5 = 1.
5. 8^(log₈ 12) = 12 по свойству a^(logₐ x) = x.
6. log₁₂ 144⁴ = log₁₂(12²)⁴ = log₁₂ 12⁸ = 8.
7. log₁₉ 1 = 0.
8. log₃ 3 = 1.
9. log₃ 13,5 + log₃ 2 = log₃ 27 = 3.
10. log₂ 64¹¹ = log₂(2⁶)¹¹ = log₂ 2⁶⁶ = 66.

Ответ: 1) log₅ 32; 2) 4; 3) 2; 4) 1; 5) 12; 6) 8; 7) 0; 8) 1; 9) 3; 10) 66.