1. If the equation $\log _{2}\left[k\left(x-\frac{1}{2}\right)\right]=2 \log _{2}\left(x+\frac{1}{2}\right)$ has only one real root, then the maximum value of $k$ that satisfies the condition is
$\qquad$ .
For $k>0$, $k\left(x-\frac{1}{2}\right)=\left(x+\frac{1}{2}\right)^{2} \Rightarrow k=\frac{\left(x+\frac{1}{2}\right)^{2}}{x-\frac{1}{2}} \xlongequal{t=x-\frac{1}{2}>0} \frac{(t+1)^{2}}{t}=t+\frac{1}{t}+2 \geqslant 4$, thus only when $k=4$, the original equation has one real root. Therefore, the maximum value of $k$ that satisfies the condition is 4.