G1.4 If $x$ is an integer satisfying $\log _{1 / 4}(2 x+1)<\log _{1 / 2}(x-1)$, find the maximum value of $x$.
$$
\begin{array}{l}
\frac{\log (2 x+1)}{\log \frac{1}{4}}2 \log (x-1) \\
2 x+1>(x-1)^{2} \\
x^{2}-4 x<0 \\
0<x<4
\end{array}
$$

The maximum integral value of $x$ is 3 .