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[tex] = {125}^{ \frac{x}{2} } . {25}^{ \frac{5x}{3} } < {625}^{ \frac{x - 2}{2} } \\ = {({5}^{3})}^{ \frac{x}{2} } . { {5}^{2} }^{ \frac{5x}{3} } < { {5}^{4} }^{ \frac{x - 2}{2} } \\ = {5}^{ \frac{3x}{2} } . {5}^{ \frac{10x}{3} } < {5}^{2x - 4} \\ \\ = > \frac{3x}{2} + \frac{10x}{3} < 2x - 4 \\ = \frac{9x + 20x}{6} < 2x - 4 \\ = \frac{29x}{6} < 2x - 4 \\ = 29x < 12x - 24 \\ =17x < - 24 \\ =x < \frac{ - 24}{17} [/tex]