Solve ln equation using subtraction law

Equation involves ln(A) - ln(B) = constant or ln expression, solved by combining into ln(A/B) and exponentiating.

12 questions · Moderate -0.5

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CAIE P2 2020 June Q1
3 marks Moderate -0.5
1 Solve the equation $$\ln ( x + 1 ) - \ln x = 2 \ln 2$$
CAIE P2 2020 November Q1
4 marks Moderate -0.5
1 Given that $$\ln ( 2 x + 1 ) - \ln ( x - 3 ) = 2$$ find \(x\) in terms of e.
CAIE P3 2014 June Q1
3 marks Moderate -0.5
1 Solve the equation \(\log _ { 10 } ( x + 9 ) = 2 + \log _ { 10 } x\).
CAIE P3 2008 November Q1
3 marks Moderate -0.5
1 Solve the equation $$\ln ( x + 2 ) = 2 + \ln x$$ giving your answer correct to 3 decimal places.
CAIE P3 2009 November Q1
4 marks Moderate -0.5
1 Solve the equation $$\ln ( 5 - x ) = \ln 5 - \ln x$$ giving your answers correct to 3 significant figures.
CAIE P3 2012 November Q1
3 marks Moderate -0.5
1 Solve the equation $$\ln ( x + 5 ) = 1 + \ln x$$ giving your answer in terms of e.
CAIE P2 2017 November Q1
4 marks Moderate -0.3
1 Solve the equation \(\ln ( 3 x + 1 ) - \ln ( x + 2 ) = 1\), giving your answer in terms of e.
CAIE P3 2023 June Q1
4 marks Moderate -0.5
1 Solve the equation \(\ln ( x + 5 ) = 5 + \ln x\). Give your answer correct to 3 decimal places.
CAIE P3 2024 June Q2
4 marks Standard +0.3
2 Solve the equation \(\ln ( x - 5 ) = 7 - \ln x\). Give your answer correct to 2 decimal places.
OCR C2 2007 January Q5
8 marks Moderate -0.8
5
    1. Express \(\log _ { 3 } ( 4 x + 7 ) - \log _ { 3 } x\) as a single logarithm.
    2. Hence solve the equation \(\log _ { 3 } ( 4 x + 7 ) - \log _ { 3 } x = 2\).
  2. Use the trapezium rule, with two strips of width 3, to find an approximate value for $$\int _ { 3 } ^ { 9 } \log _ { 10 } x \mathrm {~d} x ,$$ giving your answer correct to 3 significant figures.
OCR C2 Q1
4 marks Moderate -0.3
  1. Solve the equation
$$\log _ { 5 } ( 4 x + 3 ) - \log _ { 5 } ( x - 1 ) = 2$$
OCR C2 2016 June Q4
6 marks Moderate -0.8
4
  1. Express \(2 \log _ { 3 } x - \log _ { 3 } ( x + 4 )\) as a single logarithm.
  2. Hence solve the equation \(2 \log _ { 3 } x - \log _ { 3 } ( x + 4 ) = 2\).