Question

Решите неравенства:
1) $lg2x\ \textless \ 2lg7+1$
2) $log_2(x^2-13x+30)\ \textless \ 3$

Answer 1

1
x>0
lg2x>lg49+lg10
lg2x>lg490
2x>490
x>245
x∈(245;∞)
2
x²-13x+30>0
x1+x2=13 U x1*x2=30⇒x1=3 U x2=10
x<3 U x>10
x²-13x+30<8
x²-13x+22<0
x1+x2=13 U x1*x2=22⇒x1=2 U x1=11
2<x<11
x∈(2;3) U (10;11)