Two-part: solve then substitute

Part (a) solves a logarithmic equation, then part (b) uses that solution by substituting a trigonometric or other expression for x.

2 questions · Standard +0.0

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CAIE P2 2021 June Q1
5 marks Moderate -0.3
1
  1. Solve the equation \(\ln ( 2 + x ) - \ln x = 2 \ln 3\).
  2. Hence solve the equation \(\ln ( 2 + \cot y ) - \ln ( \cot y ) = 2 \ln 3\) for \(0 < y < \frac { 1 } { 2 } \pi\). Give your answer correct to 4 significant figures.
CAIE P2 2018 June Q4
7 marks Standard +0.3
4
  1. Solve the equation \(2 \ln ( 2 x ) - \ln ( x + 3 ) = 4 \ln 2\).
  2. Hence solve the equation $$2 \ln \left( 2 ^ { u + 1 } \right) - \ln \left( 2 ^ { u } + 3 \right) = 4 \ln 2$$ giving the value of \(u\) correct to 4 significant figures.