8. Sketch the curve \(y = 2 ^ { 2 x + 3 }\), stating the coordinates of any points of intersection with the axes. The point \(P\) on the curve \(y = 3 ^ { 3 x + 2 }\) has \(y\)-coordinate equal to 180 .
Use logarithms to find the \(x\)-coordinate of \(P\) correct to 3 significant figures. The curves \(y = 2 ^ { 2 x + 3 }\) and \(y = 3 ^ { 3 x + 2 }\) intersect at the point \(Q\).
Show that the \(x\)-coordinate of \(Q\) can be written as $$x = \frac { 3 \log _ { 3 } 2 - 2 } { 3 - 2 \log _ { 3 } 2 }$$