Помогите сделать!log(x)2-log(4)X=7/6

Question

Помогите сделать!
log(x)2-log(4)X=7/6

Answer 1

Logx_2 - 1/2* log2_x = 7/6;
1/ log2_x - 1/2* log2_x = 7/6;
log2_x = t;
1 / t - 1/2  * t - 7/6 = 0;
6 - 3 t^2 - 7 t = 0;
3 t^2 + 7t - 6 = 0;
D = 49 + 72 = 121= 11^2;
t1 = - 6; ⇒log2_x = 6;   x = 2^6 = 64;
t2 = 2/3;  ⇒ log2_x = 2/3; x = 2^(2/3)= 4^(1/3)=корень кубический из 4