Mixed exponential and e terms

Solve equations involving both general exponentials and natural exponentials, such as a^(f(x)) = be^(g(x)).

4 questions · Standard +0.0

1.06g Equations with exponentials: solve a^x = b
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CAIE P2 2024 June Q2
4 marks Standard +0.3
2 Use logarithms to solve the equation \(6 ^ { 2 x - 1 } = 5 \mathrm { e } ^ { 3 x + 2 }\). Give your answer correct to 4 significant figures. [4]
CAIE P2 2022 November Q2
4 marks Standard +0.3
2 Use logarithms to solve the equation \(14 \mathrm { e } ^ { - 2 x } = 5 ^ { x + 1 }\), giving your answer correct to 3 significant figures. [4]
CAIE P3 2014 November Q1
3 marks Moderate -0.8
1 Use logarithms to solve the equation \(\mathrm { e } ^ { x } = 3 ^ { x - 2 }\), giving your answer correct to 3 decimal places.
CAIE P2 2024 June Q2
4 marks Standard +0.3
Use logarithms to solve the equation \(6^{2x-1} = 5e^{3x+2}\). Give your answer correct to 4 significant figures. [4]