Question

32*9^x меньше или равно 60*3^X-7

Answer 1

32*(3^x)^2 ≤60*3^x  - 7;
3^x = t; 
32 t^2  - 60 t + 7  ≤ 0;
D = 3600 - 896 = 2704 = 52^2;
 t1 = 1/8;
 t2= 7/4;
(t - 1/8)(t - 7/4) ≤ 0;
1/8≤ t ≤ 7/4;
1/8 ≤ 3^x ≤ 7/4;
log3_(1/8) ≤ x ≤ log3_(7/4)