1. Let the function $f(x)=\left|\log _{2} x\right|$, and real numbers $a, b (a<b)$ satisfy
$$
\begin{array}{l}
f(a+1)=f(b+2), \\
f(10 a+6 b+22)=4 .
\end{array}
$$

Then $a b=$ . $\qquad$
$\begin{array}{l}\text {-、1. } \frac{2}{15} . \\ \text { Given } f(a+1)=f(b+2) \\ \Rightarrow\left|\log _{2}(a+1)\right|=\left|\log _{2}(b+2)\right| \text {. } \\ \text { Given } a<b \Rightarrow a+1<b+2 \text {. } \\ \text { Then }(a+1)(b+2)=1 \text {, and. } \\ 0<a+1<1<b+2 \text {. } \\ \text { Given } f(10 a+6 b+22)=4 \\ \Rightarrow 10 a+6 b+22=6(b+2)+\frac{10}{b+2}=16 \\ \Rightarrow b=-\frac{1}{3} \text { or } b=-1 \text { (discard) } \\ \Rightarrow a=-\frac{2}{5}, a b=\frac{2}{15} .\end{array}$