2026 NORTHBROOKS P1 Q12

2026 NORTHBROOKS P1 Q12

Secondary 4
5 marks
  1. Sketch the graph of \(y=\ln(x-1)\) for \(x>1\).[2]
  2. In order to solve the equation \(\mathrm e^{x-1}=\sqrt{x-1}\), a suitable straight line has to be drawn on the same set of axes as the graph of \(y=\ln(x-1)\). Find the equation of this straight line.[3]

Solution:

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Answer:(a) Increasing logarithmic branch, asymptote \(x=1\), intercept \((2,0)\). (b) \(y=2(x-1)\).

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