1. ĐKXĐ: \(x>\dfrac{4}{3}\)
\(log_2\left(3x-4\right)< 2\)
\(\Leftrightarrow log_2\left(3x-4\right)< log_24\)
\(\Leftrightarrow3x-4< 4\)
\(\Rightarrow x< \dfrac{8}{3}\)
\(\Rightarrow\dfrac{4}{3}< x< \dfrac{8}{3}\)
b.
ĐKXĐ: \(x>\dfrac{1}{2}\)
\(log_{0,3}\left(x+1\right)>log_{0,3}\left(4x-2\right)\)
\(\Leftrightarrow x+1< 4x-2\) (do \(0,3< 1\) )
\(\Leftrightarrow x>1\)
Vậy \(x>1\)
3.
ĐKXĐ: \(\left[{}\begin{matrix}-3< x< 1\\x>3\end{matrix}\right.\)
\(log\left(x^2-4x+3\right)>log\left(x+3\right)\)
\(\Leftrightarrow x^2-4x+3>x+3\)
\(\Leftrightarrow x^2-5x>0\)
\(\Rightarrow\left[{}\begin{matrix}x>5\\x< 0\end{matrix}\right.\)
Kết hợp ĐKXĐ: \(\left[{}\begin{matrix}-3< x< 0\\x>5\end{matrix}\right.\)
4.
ĐKXĐ: \(\dfrac{3}{2}< x< 2\)
\(ln\left(4-x^2\right)\le ln\left(2x-3\right)\)
\(\Leftrightarrow4-x^2\le2x-3\)
\(\Leftrightarrow x^2+2x-7\ge0\Rightarrow\left[{}\begin{matrix}x\ge-1+2\sqrt{2}\\x\le-1-2\sqrt{2}\end{matrix}\right.\)
Kết hợp ĐKXĐ: \(\Rightarrow-1+2\sqrt{2}\le x< 2\)
