If 251−x×5x+2÷(1125)x=625−1 25 1 − x × 5 x + 2 ÷ ( 1 125 ) x = 625 − 1 , find the value of x.

Question 1 Report

If $25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{- 1}$ , find the value of x.

x = -4

x = 2

x = -2

x = 4

Answer Details

$25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{- 1}$
$(5^{2})^{(1 - x)} \times 5^{(x + 2)} \div (5^{- 3})^{x} = (5^{4})^{- 1}$
$5^{2 - 2 x} \times 5^{x + 2} \div 5^{- 3 x} = 5^{- 4}$
$5^{(2 - 2 x) + (x + 2) - (- 3 x)} = 5^{- 4}$
Equating bases, we have
$2 - 2 x + x + 2 + 3 x = - 4$
$4 + 2 x = - 4 ⟹ 2 x = - 4 - 4$
$2 x = - 8$
$x = - 4$

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