Solve log equation then substitute trig/exponential expression

Part (i) solves a logarithmic equation for x, then part (ii) substitutes a trigonometric or exponential expression for x and solves the resulting equation.

3 questions · Standard +0.1

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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.
CAIE P3 2014 June Q2
4 marks Standard +0.3
Solve the equation $$2\ln(5 - e^{-2x}) = 1,$$ giving your answer correct to 3 significant figures. [4]