Question 1 - A-Level Maths

CAIE P3 2017 March — Question 1 3 marks

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2017
Session	March
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Exponential Equations & Modelling
Type	Natural logarithm equation solving
Difficulty	Moderate -0.5 This is a straightforward single-step natural logarithm equation requiring only basic manipulation: exponentiate both sides to get 1 + 2^x = e^2, rearrange to 2^x = e^2 - 1, then take log base 2. It's slightly easier than average because it's a direct application of logarithm laws with no multi-step problem-solving or conceptual challenges.
Spec	1.06g Equations with exponentials: solve a^x = b

1 Solve the equation \(\ln \left( 1 + 2 ^ { x } \right) = 2\), giving your answer correct to 3 decimal places.

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Question 1:

Answer	Marks	Guidance
Answer	Mark	Guidance
Remove logarithm and obtain \(1 + 2^x = e^2\)	B1
Use correct method to solve equation of the form \(2^x = a\), where \(a > 0\)	M1
Obtain answer \(x = 2.676\)	A1

Total: 3

## Question 1:

| Answer | Mark | Guidance |
|--------|------|----------|
| Remove logarithm and obtain $1 + 2^x = e^2$ | B1 | |
| Use correct method to solve equation of the form $2^x = a$, where $a > 0$ | M1 | |
| Obtain answer $x = 2.676$ | A1 | |

**Total: 3**

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1 Solve the equation $\ln \left( 1 + 2 ^ { x } \right) = 2$, giving your answer correct to 3 decimal places.\\

\hfill \mbox{\textit{CAIE P3 2017 Q1 [3]}}

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