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If frac 27 x times 3 1 - x 9 2x 1 find the valu... - WAEC Mathematics 2015 Question

If (\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1), find the value of x.

A
1
B
\(\frac{1}{2}\)
C
-\(\frac{1}{2}\)
D
-1
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Correct Option: B

(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1)

(\frac{3^{3x} \times 3^{1 - x}}{3^{2(2 - x)}} = 3^0)

(3^{3x} \times 3^{1 - x} \div 3^{4x} = 3^0)

(3^{(3x + 1 - x - 4x)} = 3^0)

(3^{(1 - 2x)} = 3^0)

since the bases are equal,

1 - 2x = 0

  • 2x = -1

x = (\frac{1}{2})

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