Express y in terms of x (ln/log equations)

Given an equation with natural or general logarithms involving two variables, apply log laws to express one variable explicitly in terms of the other without logarithms, where the result is a straightforward algebraic rearrangement.

5 questions · Standard +0.0

Sort by: Default | Easiest first | Hardest first

CAIE P3 2013 June Q2

4 marks Standard +0.3

2 It is given that \(\ln ( y + 1 ) - \ln y = 1 + 3 \ln x\). Express \(y\) in terms of \(x\), in a form not involving logarithms.

CAIE P3 2013 November Q1

4 marks Standard +0.3

1 Given that \(2 \ln ( x + 4 ) - \ln x = \ln ( x + a )\), express \(x\) in terms of \(a\).

CAIE P2 2009 November Q2

4 marks Moderate -0.5

2 It is given that \(\ln ( y + 5 ) - \ln y = 2 \ln x\). Express \(y\) in terms of \(x\), in a form not involving logarithms.

Edexcel C2 2014 January Q6

5 marks Standard +0.3

6. Given that $$\log _ { x } ( 7 y + 1 ) - \log _ { x } ( 2 y ) = 1 , \quad x > 4 , \quad 0 < y < 1$$ express \(y\) in terms of \(x\).

OCR MEI C3 Q5

4 marks Moderate -0.3

Make \(x\) the subject of \(t = \ln \sqrt{\frac{5}{(x-3)}}\). [4]