Question

найдите неравенство $lg^{2} 100x-7lgx\geq 8$

Answer 1

lg²100x - 7lgx >= 8

(lgx+lg100)²-7lgx >= 8

lg²x+4lgx+4-7lgx-8 >= 0

lg²x-3lgx-4 >= 0

lg²x+lgx-4lgx-4 >= 0

lgx(lgx+1)-4(lgx+1) >= 0

(lgx+1)(lgx-4) >= 0

+. -. +

------[-1]--------[4]------

[lg x <= -1

[lg x >= 4

[0 < x <= 1/10

[x >= 10000

Ответ: x€(0: 0.1)U[10000; + ∞)