Question

$25 {}^{x - 1 = } 5 {}^{2x - 1} - 100$
Please solve it ​

Answer 1

Answer:

 25^x-1 = 5^(2x-1) - 100

⇒ 5^2x-2 = 5^(2x-1) - 100

⇒ 5^2x-2 - 5^2x-1 = -100

⇒ 5^2x [ 5^-2 - 5^-1] = - 100

⇒ 5^2x [ 1  -  1 ]  = - 100

             25    5

⇒ 5^2x [ 1 - 5]  = - 100

               25

⇒ 5^2x [ -4 ] = - 100

              25

⇒ 5^2x [-4] = -100 * 25

⇒ 5^2x = 100 * 25     [ - * - = +]

                  4 

⇒ 5^2x = 625

⇒ 5^2x  = 5^4 

so, ⇒  2x = 4

      ⇒  x = 2

Answer 2

Answer:

x = 2

For solution , please refer to the attachment.