$Thedomainoff\left(x\right)=\log [{\left(2.5\right)}^{3-x^2}-{\left(0.4\right)}^{x+9}]$

$$\begin{gathered} \begin{array}{l}f\left(x\right)=\log [{\left(2.5\right)}^{3-x^2}-{\left(0.4\right)}^{x+9}]isdefined\\ iff{\left(2.5\right)}^{3-x^2}-{\left(0.4\right)}^{x+9}>0\end{array} \\ \Rightarrow {\left(\frac{5}{2}\right)}^{3-x^2}>{\left(\frac{2}{5}\right)}^{x+9} \\ \Rightarrow 3-x^2=-x-9 \\ \Rightarrow x^2-x-12<0 \\ \Rightarrow (x+3)(x-4)<0 \\ \Rightarrow -3<x<4 \end{gathered}$$