CAIE P3 2019 June — Question 1 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2019
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyModerate -0.8 This is a straightforward exponential equation requiring a standard technique: take logarithms of both sides, apply log laws, and solve the resulting linear equation. It's routine A-level work with no conceptual challenges, making it easier than average, though not trivial since it requires careful algebraic manipulation.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b

1 Use logarithms to solve the equation \(5 ^ { 3 - 2 x } = 4 \left( 7 ^ { x } \right)\), giving your answer correct to 3 decimal places.

Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Use law of the logarithm of a product or quotientM1
Use law of the logarithm of power twiceM1
Obtain a correct linear equation in \(x\), e.g. \((3-2x)\ln 5 = \ln 4 + x\ln 7\)A1
Obtain answer \(x = 0.666\)A1
Total4
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| Use law of the logarithm of a product or quotient | M1 | |
| Use law of the logarithm of power **twice** | M1 | |
| Obtain a correct linear equation in $x$, e.g. $(3-2x)\ln 5 = \ln 4 + x\ln 7$ | A1 | |
| Obtain answer $x = 0.666$ | A1 | |
| **Total** | **4** | |

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1 Use logarithms to solve the equation $5 ^ { 3 - 2 x } = 4 \left( 7 ^ { x } \right)$, giving your answer correct to 3 decimal places.\\

\hfill \mbox{\textit{CAIE P3 2019 Q1 [4]}}