Решение
1) 3 /log₃ 3 - 2/[2*log₂³ 2] - 1/[1/4*log₃³ 3] = 3 - [2/(2/3)*log₂ 2] - [1/(4/3)log₃ 3] =
= 3 - 3 - 3/4 = - 3/4
2) (lg 2 + lg 3)/(lg(3,6) + lg10) = lg(2*3) / lg(3,6*10) = lg6/lg36 = lg6/lg6² =
= lg6/(2*lg6) = 1/2
3) 2^(2 - log₂ 5) + (1/2)^log₂ 5 = 2² / 2^(log₂ 5) + 2^(log₂ 5⁻¹) = 4/5 + 1/5 = 1
4) 3^(2 + log₃ 4) + (1/3)^log₃ 4 = 3² * 3^(log₃ 4) + 3^(log₃ 4⁻¹) =
= 9*4 + 1/4 = 36 + 1/4 = 36(1/4)