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5^2x - 1 - 25 ^x - 1 = 2500
5^2x × 5^-1 - 5^2x × 5^-2= 2500
5^2x ( 5^-1 - 5 ^ -2 ) = 2500
5^2x ( 1/5 - 1/25 ) = 2500
5^2x × 4/25 = 2500
5^2x = 2500 × 25/4
5^2x = 625 × 25
5^2x = 5^4 × 5^2
5^2x = 5^6
2x = 6
x = 3
5^2x × 5^-1 - 5^2x × 5^-2= 2500
5^2x ( 5^-1 - 5 ^ -2 ) = 2500
5^2x ( 1/5 - 1/25 ) = 2500
5^2x × 4/25 = 2500
5^2x = 2500 × 25/4
5^2x = 625 × 25
5^2x = 5^4 × 5^2
5^2x = 5^6
2x = 6
x = 3
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