Edexcel C2 2007 January — Question 4 3 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2007
SessionJanuary
Marks3
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Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyEasy -1.2 This is a straightforward one-step exponential equation requiring only taking logarithms of both sides and dividing. It's a direct application of a standard technique with no problem-solving or multi-step reasoning required, making it easier than average but not trivial since students must recall the logarithm method.
Spec1.06g Equations with exponentials: solve a^x = b
4. Solve the equation $$5 ^ { x } = 17$$ giving your answer to 3 significant figures.
Question 4:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(x\log 5 = \log 17\) or \(x = \log_5 17\)M1 Acceptable alternatives: \(x\log_{10}5 = \log_{10}17\); \(x\ln 5 = \ln 17\) etc.
\(x = \frac{\log 17}{\log 5}\)A1 Exact expression evaluable on calculator; can be implied by correct final answer
\(= 1.76\)A1 (3) 1.76 cao; answer to greater accuracy but rounds to 1.76: M1 A1 A0; answer only 1.8: M1 A1 A0 
## Question 4:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $x\log 5 = \log 17$ or $x = \log_5 17$ | M1 | Acceptable alternatives: $x\log_{10}5 = \log_{10}17$; $x\ln 5 = \ln 17$ etc. |
| $x = \frac{\log 17}{\log 5}$ | A1 | Exact expression evaluable on calculator; can be implied by correct final answer |
| $= 1.76$ | A1 **(3)** | 1.76 cao; answer to greater accuracy but rounds to 1.76: M1 A1 A0; answer only 1.8: M1 A1 A0 |

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4. Solve the equation

$$5 ^ { x } = 17$$

giving your answer to 3 significant figures.\\

\hfill \mbox{\textit{Edexcel C2 2007 Q4 [3]}}
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