Express y in terms of x (requires exponentiating both sides)

Given a logarithmic equation where one side is a single log or constant, exponentiate to remove logarithms and then rearrange to express one variable in terms of the other, typically involving e^x or a^x in the result.

4 questions · Moderate -0.4

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CAIE P3 2016 November Q1

3 marks Moderate -0.5

1 It is given that \(z = \ln ( y + 2 ) - \ln ( y + 1 )\). Express \(y\) in terms of \(z\).

CAIE P3 2019 November Q1

3 marks Standard +0.3

1 Given that \(\ln \left( 1 + \mathrm { e } ^ { 2 y } \right) = x\), express \(y\) in terms of \(x\).

CAIE P3 2023 March Q1

3 marks Moderate -0.5

1 It is given that \(x = \ln ( 2 y - 3 ) - \ln ( y + 4 )\).
Express \(y\) in terms of \(x\).

CAIE P3 2006 June Q1

3 marks Moderate -0.8

Given that \(x = 4(3^{-y})\), express \(y\) in terms of \(x\). [3]