On a single diagram, sketch the curves with the following equations. In each case state the coordinates of any points of intersection with the axes.
(a) \(y = a ^ { x }\), where \(a\) is a constant such that \(a > 1\).
(b) \(y = 2 b ^ { x }\), where \(b\) is a constant such that \(0 < b < 1\).
The curves in part (i) intersect at the point \(P\). Prove that the \(x\)-coordinate of \(P\) is
$$\frac { 1 } { \log _ { 2 } a - \log _ { 2 } b } .$$