Question

help me

x^2 - 5x+6 < ( 2-x) log\(^x_2\)

Answer 1

ta có : \(\left(2-x\right)\log_2x>x^2-5x+6\) \(\left(đk:x>0\right)\)

\(\Leftrightarrow\left(2-x\right)\log_2x>\left(2-x\right)\left(3-x\right)\) (1)

th1) \(x< 2\) \(\left(1\right)\Leftrightarrow\log_2x>3-x\Leftrightarrow x>2^{3-x}>2^{3+2}\Leftrightarrow x>32\left(loại\right)\)

th2) \(x>2\) \(\left(1\right)\Leftrightarrow\log_2x< 3-x\Leftrightarrow x< 2^{3-x}< 2^{3+2}\Leftrightarrow x< 32\)

kết hợp điều kiện ta có \(2< x< 32\)

vậy \(2< x< 32\) .