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Equating the bases, we get,
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$$\begin{lgathered}{( - \frac{5}{8} )}^{x - 9} = 1 \\ = > {( - \frac{5}{8} )}^{x - 9} = {( - \frac{5}{8} )}^{0} [∵ {a}^{0} = 1]\end{lgathered}$$
Equating the bases, we get,
$$\begin{lgathered}x - 9 = 0 \\ = > x = \small\sf\red{9}\end{lgathered}$$
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