13. Let $f(x)=\lg \frac{1+2^{x}+4^{x} \cdot a}{3}$, where $a \in \mathbf{R}$. If $f(x)$ is defined for $x \in(-\infty, 1)$, find the range of values for $a$.
13. $1+2^{x}+4^{x} a>0$, i.e., $a>-\left(\frac{1}{4}\right)^{x}-\left(\frac{1}{2}\right)^{x}, x \in(-\infty, 1)$. Let $g(x)=-\left(\frac{1}{4}\right)^{x}-\left(\frac{1}{2}\right)^{x}$, it is easy to see that $g(x)$ is an increasing function, then $g(x)<g(1)=-\frac{3}{4}$, hence $a \geqslant-\frac{3}{4}$.