Question

If 5^2x-1 - (25)^x-1 = 2500, then find the value of x.

Answer 1

$\Huge{\red{\underline{\textsf{Answer}}}}$

⇝$5^{(2x - 1)} - 25^{x - 1} = 2500$

⇝$5^{(2x - 1)} - 5^{2}^{(x - 1)} = 5^{2} \times 5^{2} \times 2^{2}$

⇝$5^{(2x - 1)} - 5^{2x - 2} = 5^{4} \times 2^{2}$

⇝$5^{(2x - 1)}(1 - 5^{ - 1}) = 5^{4} \times 2^{2}$

⇝$5^{(2x - 1)} (1 - \frac{1}{5}) = 5 ^{4} \times 2^{2}$

⇝$5^{(2x - 1)}( \frac{4}{5}) = 5^{4} \times 2^{2}$

⇝$5^{(2x - 1)} = 5^{5}$

Comparing both sides

$\implies\rm 2x - 1 = 5$

$\implies\rm 2x = 6$

$\implies\rm x = 3$