2025 NASS P2 Q6

2025 NASS P2 Q6

Secondary 4
10 marks

It is given that \(y=2\log_w(wx)+\log_w(3x-2)-2\), where \(w\) is a positive integer and \(w\ne1\).

  1. Write down the range of values of \(x\) for which \(y\) is defined.[1]
  2. Show that \(y\) can be written as \(\log_w(3x^3-2x^2)\).[4]
  3. Hence show that \(y=0\) has only one real root.[5]

Solution:

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Answer:(a) \(x>\dfrac23\); (b) \(y=\log_w(3x^3-2x^2)\); (c) only real root \(x=1\).

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