Question on: JAMB Mathematics - 2024
If \(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\), find the value of x.
A
x = -4
B
x = 2
C
x = -2
D
x = 4
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Correct Option: A
We are given the equation: \(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\). Start by expressing all numbers in terms of base 5:
- \(25 = 5^2\), so \(25^{1 - x} = 5^{2(1 - x)} = 5^{2 - 2x}\)
- \(125 = 5^3\), so \((1/125)^x = (5^{-3})^x = 5^{-3x}\)
- \(625 = 5^4\), so \(625^{-1} = 5^{-4}\)
Now, the equation becomes: \(5^{2 - 2x} \times 5^{x + 2} \div 5^{-3x} = 5^{-4}\).
Combine the exponents: \(5^{2 - 2x + x + 2 + 3x} = 5^{4 + 2x}\)
Set the exponents equal: 4 + 2x = -4, hence 2x = -8 and x = -4.
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