If \(\frac{27^x \times 3^{1 – x}}{9^{2x}} = 1\), find the value of x.
- 1
-
\(\frac{1}{2}\)
- -\(\frac{1}{2}\)
- -1
The correct answer is: B
Explanation
\(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1\)\(\frac{3^{3x} \times 3^{1 - x}}{3^{2(2 - x)}} = 3^0\)
\(3^{3x} \times 3^{1 - x} \div 3^{4x} = 3^0\)
\(3^{(3x + 1 - x - 4x)} = 3^0\)
\(3^{(1 - 2x)} = 3^0\)
since the bases are equal,
1 - 2x = 0
- 2x = -1
x = \(\frac{1}{2}\)