Sketch the curve with equation \(y = 7 ^ { x }\), indicating the coordinates of any point where the curve intersects the coordinate axes.
The curve \(C _ { 1 }\) has equation \(y = 7 ^ { x }\).
The curve \(C _ { 2 }\) has equation \(y = 7 ^ { 2 x } - 12\).
By forming and solving a quadratic equation, prove that the curves \(C _ { 1 }\) and \(C _ { 2 }\) intersect at exactly one point. State the \(y\)-coordinate of this point.
Use logarithms to find the \(x\)-coordinate of the point of intersection of \(C _ { 1 }\) and \(C _ { 2 }\), giving your answer to three significant figures.
(2 marks)