Решите пожалуйста ^_^

Ответ
1) log(1/V2) 4*кубV32 =
___ 1/V2 = 2^(-1/2)
___ кубV32 = 32^(1/3) = (2^5)^(1/3) = 2^(5*1/3) = 2^(5/3)
___ 4 = 2^2
= log(2^(-1/2)) (2^2)*2^(5/3) =
= 1/ (-1/2) * log(2) 2^(2+5/3) =
= (-2) * log(2) 2^(11/3) =
= (-2) * (11/3) * log(2) 2 = -22/3

2) 49^(log7 3 + 1) =
= 49^(log7 3) * 49^1 =
= (7^2)^log7 3 * (7^2) =
= 7^(2log7 3) * (7^2) =
= 7^(log7 3^2) * (7^2)) =
= 3^2 * 7^2 =
= (3*7)^2 = 21^2 = 441

3) log3 (2x+1) + log3 (x-3) = 2
log3 (2x-1)*(x-3) = 2
(2x-1)(x-3) = 3^2
2x^2 -x-6x+3 = 9
2x^2 -7x -6 = 0 - дальше легко.

4) (log2 x)^2 + 4*log2 (2x) - 9 = 0
(log2 x)^2 + 4*[log2 2 + log2 x] - 9 = 0
(log2 x)^2 + 4*[1 + log2 x] - 9 = 0
(log2 x)^2 + 4 + 4*log2 x - 9 = 0
(log2 x)^2 + 4*log2 x - 5 = 0
log2 x = t
t^2 + 4t - 5 = 0
t1 = -5 => log2 x = -5 => x=2^(-5) = 1/2^5 = 1/32
t2 = 1 => log2 x = 1 => x=2^1 = 2