ĐK: $x>0$.
Bất phương trình tương đương với:
$\dfrac{\ln x}{2\ln 2}.\dfrac{\ln x}{\ln\dfrac{3}{4}}+3>\dfrac{3\ln x}{2\ln 2}+\dfrac{\ln x}{\ln\dfrac{3}{4}}$
$\Leftrightarrow \ln^2x+6\ln2\ln\dfrac{3}{4}<3\ln\dfrac{3}{4}\ln x+2\ln2\ln x$
$\Leftrightarrow \ln^2x-\ln\dfrac{27}{16}\ln x+\ln4\ln\dfrac{27}{64}<0$
$\Leftrightarrow (\ln x - \ln 4)(\ln x-\ln\dfrac{27}{64})<0$
$\Leftrightarrow \ln\dfrac{27}{64}<\ln x<\ln 4$
$\Leftrightarrow \dfrac{27}{64}<x<4$