Question

If 25^x-1 = 5^2x–1 - 100, then find x.​

Answer 1

25^(x -1 ) = 5^(2x - 1) - 100

=> 5^2(x-1)=5^(2x-1) -100

=> 5^(2x-2 ) = 5^(2x-1) -100.

(5^2x)/25=(5^2x)/5 - 100

(5^2x)(1/25–1/5)=-100

(5^2x)(-4/25)=-100

(5^2x)=100×25/4= 25×25=5^4

Equating exponents on both sides, we get

=> 2x = 4

=> x=4/2=2. Answer.

Answer 2

Answer:

x = 2

Step-by-step explanation:

25^(x -1 ) = 5^(2x - 1) - 100

=> 5^2(x-1)=5^(2x-1) -100

=> 5^(2x-2 ) = 5^(2x-1) -100.

(5^2x)/25=(5^2x)/5 - 100

(5^2x)(1/25–1/5)=-100

(5^2x)(-4/25)=-100

(5^2x)=100×25/4= 25×25=5^4

Equating exponents on both sides, we get

=> 2x = 4

=> x=4/2

=2 Ans.

Hope it helps you..

Please mark it as Brainliest...