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\includegraphics[max width=\textwidth, alt={}, center]{b2c1188d-881e-4fb5-bece-5a51006543c7-4_524_822_274_609}
The diagram shows the curves \(y = a ^ { x }\) and \(y = 4 b ^ { x }\).
- (a) State the coordinates of the point of intersection of \(y = a ^ { x }\) with the \(y\)-axis.
(b) State the coordinates of the point of intersection of \(y = 4 b ^ { x }\) with the \(y\)-axis.
(c) State a possible value for \(a\) and a possible value for \(b\). - It is now given that \(a b = 2\). Show that the \(x\)-coordinate of the point of intersection of \(y = a ^ { x }\) and \(y = 4 b ^ { x }\) can be written as
$$x = \frac { 2 } { 2 \log _ { 2 } a - 1 } .$$