Question

5^2x-1+25^x-1=2500 then find the value o f x

Answer 1

$given \\ {5}^{2x - 1} + {25}^{x - 1} = 2500 \\ {5}^{2x - 1} + {5}^{2(x - 1)} = 5 \times 5 \times 5 \times 2 \times 2 \\ {5}^{2x - 1 } + {5}^{2x - 2} = {5}^{3} \times {2}^{2 } \\ 2x - 1 + 2x - 2 = 3 \\ 4x - 3 = 3 \\ 4x = 6 \\ x = \frac{3}{2}$