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
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 = \(\frac{1}{2}\)
\(\frac{3^{3x} \times 3^{1 - x}}{3^{2(2 - x)}} = 3^0\)
\(3^{3x} \times 3^{1 - x} \div 3^{4x} = 3^0\)
\(3^{(3x + 1 - x - 4x)} = 3^0\)
\(3^{(1 - 2x)} = 3^0\)
since the bases are equal,
1 - 2x = 0
- 2x = -1
x = \(\frac{1}{2}\)
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