Решите логарифмические выражения из Варианта 1.

1. log_2(16) - log_2(36) = log_2(16/36) = log_2(4/9) = log_2(2^2/3^2) = log_2(2^2) - log_2(3^2) = 2log_2(2) - 2log_2(3) = 2 - 2log_2(3). 2. 6 · 7 · log_2(2) = 6 · 7 · 1 = 42. 3. 16^(3/4) = (2^4)^(3/4) = 2^(4·3/4) = 2^3 = 8. 4. log_2(2^58) = 58log_2(2) = 58. 5. log_2(270) - log_2(7·5) = log_2(270/35) = log_2(54/7). 6. log_8(512) = log_8(8^3) = 3. 7. log_2(10) - log_2(2) = log_2(10/2) = log_2(5). 8. log_8(3√3) = log_8(3^(1/3)). 9. log_2(√13) = log_2(13^(1/2)) = 1/2log_2(13). 10. log_2(18)/(2 + log_2(2^2)) = log_2(18)/4 = (log_2(2) + log_2(9))/4 = (1 + 2log_2(3))/4. 11. log_2^2(7/49) = (log_2(7/49))^2 = (log_2(7) - log_2(49))^2 = (log_2(7) - 2log_2(7))^2 = (-log_2(7))^2 = (log_2(7))^2. 12. 5^3 + log_2(2) = 125 + 1 = 126. 13. log_8(25). 14. log_1 1/18 = log_1(1) - log_1(18) = 0.