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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