Question

find the value of x :- 5^2x-1 - 25^x-1 = 2500

Answer 1

The correct problem is given here. there is no leading - in the beginning.

$+ 5^{2x-1} - 25^{x-1} = 2500 \\ \\ + 5^{2x-1} - 5^{2x-2} = 5^2 * 25 * 4 \\ \\ + 5^{2x-1} [1 - 5^{-1}] = 5^4 * 2^2 \\ \\ 5^{(2x-1)} \frac{4}{5} = 5^4 2^2 \\ \\ 5^{2x-1} = 5^5 \\ 2x -1 = 5 \\ x = 3$

Answer 2

Answer :

x = 3

Step-by-step explanation :

$5^{(2x - 1)} -25^{x - 1}=2500\\\\ 5^{(2x - 1)} -5^{2(x - 1)}=5^2 * 5^2 * 2^2\\\\ 5^{(2x - 1)} -5^{2x - 2}=5^4 * 2^2\\\\ 5^{(2x - 1)} [ 1 - 5^{- 1}] = 5^4 * 2^2\\\\5^{(2x - 1)} [ 1 - \frac{1}{5} ] = 5^4 * 2^2\\\\5^{(2x - 1)} ( \frac{4 }{5}) = 5^4 * 2^2\\\\ 5^{(2x - 1)} = 5^5$

On comparing both the sides ;

2x - 1 = 5

⇒ 2x = 5 + 1

⇒ 2x = 6

⇒ x = 3

Hence, the value of x is 3.