Question

Find the value of x, if

(5/7)^5+x × (25/49)^x =(7/5)^2​

Answer 1

$( \frac{5}{7} ) {}^{5 + x} \times ( \frac{25}{49}) {}^{x} = (\frac{7}{5})^{2} \\ ( \frac{5}{7} )^{5 + x} \times \sqrt{ (\frac{25}{49}) {}^{x}} =( \frac{7}{5})^{2} \\ \\ ( \frac{5}{7} ) {}^{5 + x + x} = (\frac{7}{5})^{2} \\ \sf \cancel\frac{5}{7} {}^{5 + 2x} = \sf \cancel\frac{7}{5}^{2} \\ 5 + 2x = 2 \\ 2x = 5 - 2 \\ 2x = 3 \\ x = \frac{3}{2}$