সহায়িকা

\begin{aligned}
\text{প্রদত্ত সমীকরণ: } & \left(\frac{a}{b}\right)^{x-3} = \left(\frac{b}{a}\right)^{x-5} \\
\text{বা, } & \left(\frac{a}{b}\right)^{x-3} = \left\{ \left(\frac{a}{b}\right)^{-1} \right\}^{x-5} \\
\text{বা, } & \left(\frac{a}{b}\right)^{x-3} = \left(\frac{a}{b}\right)^{-(x-5)} \\
\text{বা, } & \left(\frac{a}{b}\right)^{x-3} = \left(\frac{a}{b}\right)^{-x+5} \\
\text{যেহেতু ভিত্তি সমান, তাই: } & x - 3 = -x + 5 \\
\text{বা, } & x + x = 5 + 3 \\
\text{বা, } & 2x = 8 \\
\text{বা, } & x = \frac{8}{2} \\
\therefore & x = 4
\end{aligned}

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