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If \(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{...

If 251x×5x+2÷(1125)x=6251, find the value of x.

A.

x = -4

B.

x = 2

C.

x = -2

D.

x = 4

Correct answer is A

251x×5x+2÷(1125)x=6251

(52)(1x)×5(x+2)÷(53)x=(54)1

522x×5x+2÷53x=54

5(22x)+(x+2)(3x)=54

Equating bases, we have

22x+x+2+3x=4

4+2x=42x=44

2x=8

x=4