Inequalities Logarithm

Let $f(x) = \arccos (13x-8)$ , and denote $D_f$ as the domain of $f(x)$ for real $x$ .

If the range of $\large A = \left \{ x \in D_f \left | 2^{2\log_{10} (3x-2)} < (0.25)^{\log_{0.1} (3-4x) } \right . \right \}$

can be expressed as $(a,b ]$ , find the product $13ab$ .