1.06f Laws of logarithms: addition, subtraction, power rules

453 questions

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Pre-U Pre-U 9794/2 2010 June Q2
5 marks Standard +0.8
Solve the inequality $$\log_3(2x^2 - x) - \log_3(2x^2 - 3x + 1) > 1.$$ [5]
Pre-U Pre-U 9794/1 2011 June Q4
6 marks Moderate -0.8
  1. Show that \(4 \ln x - \ln(3x - 2) - \ln x^2 = \ln\left(\frac{x^2}{3x - 2}\right)\), where \(x > \frac{2}{3}\). [3]
  2. Hence solve the equation \(4 \ln x - \ln(3x - 2) - \ln x^2 = 0\). [3]
Pre-U Pre-U 9794/2 2012 June Q4
4 marks Easy -1.2
Use logarithms to solve the equation \(2^{2x-1} = 5\). [4]