Answer: x = 1
1. We need to simplify 9 into \(3^{2}\), and 27 into \(3^{3}\):
\(9^{(7 - x)} = 27^{(4x)} =
\\ \\ \\
(3^{2})^{(7 - x)} = (3^{3})^{(4x)} =
\\ \\ \\
3^{(14 - 2x)} = 3^{(12x)}\).
2. We re left with
14 - 2x = 12x
-2x = 12x - 14
-14x = -14 |:(-14)
X = 1
So answer is x = 1. Proof:
\(9^{7 - 1} = 27^{4} \\ \\ \\
9^{6} = 27^{4} \\ \\ \\
(3^{2})^{6} = (3^{3})^{4} \\ \\ \\
3^{12} = 3^{12}\).
And if both sides are equal equation is right. Hope it helps!