Inequalities Logarithm

Algebra Level 3

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 $$13ab$$.

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