Question

help me

1, tìm m đẻ bpt sau t/m x thuộc ( 2;3)

log\(^{x^2+4x+m}_5\) - log\(^{x^2+1}_5\)\(\le1\)

-2. giải bpt

log \(^{\left(x-\dfrac{1}{4}\right)}_x\ge2\)

Answer 1

bài 1 mk o bt lm ; nên mk lm câu 2 thôi nha .

bài 2) ta có : \(\log_x\left(x-\dfrac{1}{4}\right)\ge2\Leftrightarrow x-\dfrac{1}{4}\ge x^2\Leftrightarrow x^2-x+\dfrac{1}{4}\le0\)

\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2\le0\)

mà ta có : \(\left(x-\dfrac{1}{2}\right)^2\ge0\forall x\)

\(\Rightarrow0\le\left(x-\dfrac{1}{2}\right)^2\le0\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2=0\) \(\Leftrightarrow x=\dfrac{1}{2}\)

vậy \(x=\dfrac{1}{2}\)