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\includegraphics[max width=\textwidth, alt={}, center]{87012792-fa63-4003-875d-b8e7739037f1-4_489_697_274_667}
The diagram shows the curves \(y = \log _ { 2 } x\) and \(y = \log _ { 2 } ( x - 3 )\).
- Describe the geometrical transformation that transforms the curve \(y = \log _ { 2 } x\) to the curve \(y = \log _ { 2 } ( x - 3 )\).
- The curve \(y = \log _ { 2 } x\) passes through the point ( \(a , 3\) ). State the value of \(a\).
- The curve \(y = \log _ { 2 } ( x - 3 )\) passes through the point ( \(b , 1.8\) ). Find the value of \(b\), giving your answer correct to 3 significant figures.
- The point \(P\) lies on \(y = \log _ { 2 } x\) and has an \(x\)-coordinate of \(c\). The point \(Q\) lies on \(y = \log _ { 2 } ( x - 3 )\) and also has an \(x\)-coordinate of \(c\). Given that the distance \(P Q\) is 4 units find the exact value of \(c\).