Solve ln equation using power law

Equation involves terms like 2ln(x) or coefficients on logarithms, solved by applying power law to move coefficients inside as exponents.

15 questions · Standard +0.1

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CAIE P2 2013 June Q2
5 marks Standard +0.3
2 Solve the equation \(\ln ( 3 - 2 x ) - 2 \ln x = \ln 5\).
CAIE P3 2012 June Q1
4 marks Moderate -0.3
1 Solve the equation $$\ln ( 3 x + 4 ) = 2 \ln ( x + 1 )$$ giving your answer correct to 3 significant figures.
CAIE P3 2012 June Q2
4 marks Moderate -0.3
2 Solve the equation \(\ln ( 2 x + 3 ) = 2 \ln x + \ln 3\), giving your answer correct to 3 significant figures.
CAIE P3 2015 June Q1
4 marks Moderate -0.3
1 Solve the equation \(\ln ( x + 4 ) = 2 \ln x + \ln 4\), giving your answer correct to 3 significant figures.
CAIE P3 2017 June Q1
3 marks Standard +0.3
1 Solve the equation \(\ln \left( x ^ { 2 } + 1 \right) = 1 + 2 \ln x\), giving your answer correct to 3 significant figures.
CAIE P3 2019 June Q2
4 marks Standard +0.3
2 Showing all necessary working, solve the equation \(\ln ( 2 x - 3 ) = 2 \ln x - \ln ( x - 1 )\). Give your answer correct to 2 decimal places.
CAIE P3 2016 March Q1
3 marks Standard +0.3
1 Solve the equation \(\ln \left( x ^ { 2 } + 4 \right) = 2 \ln x + \ln 4\), giving your answer in an exact form.
CAIE P2 2016 March Q3
5 marks Standard +0.3
3 It is given that \(k\) is a positive constant. Solve the equation \(2 \ln x = \ln ( 3 k + x ) + \ln ( 2 k - x )\), expressing \(x\) in terms of \(k\).
CAIE P2 2017 March Q1
5 marks Standard +0.3
1 Solve the equation \(2 \ln ( 2 x ) - \ln ( x + 3 ) = \ln ( 3 x + 5 )\).
CAIE P2 2009 November Q2
4 marks Moderate -0.3
2 Solve the equation \(\ln \left( 3 - x ^ { 2 } \right) = 2 \ln x\), giving your answer correct to 3 significant figures.
CAIE P2 2011 November Q3
5 marks Standard +0.3
3 Solve the equation \(2 \ln ( x + 3 ) - \ln x = \ln ( 2 x - 2 )\).
CAIE P3 2023 June Q2
3 marks Standard +0.3
2 Solve the equation \(\ln \left( 2 x ^ { 2 } - 3 \right) = 2 \ln x - \ln 2\), giving your answer in an exact form.
CAIE P3 2020 March Q2
4 marks Moderate -0.3
2 Solve the equation \(\ln 3 + \ln ( 2 x + 5 ) = 2 \ln ( x + 2 )\). Give your answer in a simplified exact form.
CAIE P3 2021 March Q1
3 marks Standard +0.3
1 Solve the equation \(\ln \left( x ^ { 3 } - 3 \right) = 3 \ln x - \ln 3\). Give your answer correct to 3 significant figures.
CAIE P3 2022 November Q1
4 marks Standard +0.3
1 Solve the equation \(\ln ( 2 x - 1 ) = 2 \ln ( x + 1 ) - \ln x\). Give your answer correct to 3 decimal places.