Question

Find the value of x( 5/13) -⁵ × (5/13) -¹⁰ = (5/13) ⁸x +1​

Answer 1

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$\longrightarrow \sf \bigg({ \frac{5}{13} \bigg)}^{ - 5} \times \bigg({ \frac{5}{13} \bigg)}^{ - 10} = \bigg({ \frac{5}{13} \bigg)}^{8x + 1} \\ \\\longrightarrow \sf \bigg({ \frac{5}{13} \bigg)}^{ - 5 - 10} = \bigg({ \frac{5}{13} \bigg)}^{ 8x + 1} \\ \\\longrightarrow \sf \bigg({ \frac{5}{13} \bigg)}^{ - 15} = \bigg({ \frac{5}{13} \bigg)}^{8x + 1} \\ \\\longrightarrow \sf - 15 = 8x + 1 \\ \\\longrightarrow \sf 8x = - 15 - 1 \\ \\ \longrightarrow \sf8x = - 16 \\ \\\longrightarrow \sf x = - \frac{16}{8} \\ \\\longrightarrow \boxed{ \sf x = - 2}$