CAIE P3 2017 November — Question 2 5 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2017
SessionNovember
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve log equation reducing to quadratic
DifficultyStandard +0.3 This is a straightforward logarithm equation requiring manipulation of log laws (bringing terms to one side, using power and quotient rules) and solving a resulting quadratic equation. While it involves logs to base 2 rather than natural logs, the technique is standard A-level fare with no novel insight required, making it slightly easier than average.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b

2 Showing all necessary working, solve the equation \(2 \log _ { 2 } x = 3 + \log _ { 2 } ( x + 1 )\), giving your answer correct to 3 significant figures.

Question 2:
AnswerMarks Guidance
AnswerMark Notes
Use law for the logarithm of a power or a quotient on the given equationM1
Use \(\log_2 8 = 3\) or \(2^3 = 8\)M1
Obtain \(x^2 - 8x - 8 = 0\), or horizontal equivalentA1
Solve a 3-term quadratic equationM1
Obtain final answer \(x = 8.90\) onlyA1
## Question 2:
| Answer | Mark | Notes |
|--------|------|-------|
| Use law for the logarithm of a power or a quotient on the given equation | M1 | |
| Use $\log_2 8 = 3$ or $2^3 = 8$ | M1 | |
| Obtain $x^2 - 8x - 8 = 0$, or horizontal equivalent | A1 | |
| Solve a 3-term quadratic equation | M1 | |
| Obtain final answer $x = 8.90$ only | A1 | |
2 Showing all necessary working, solve the equation $2 \log _ { 2 } x = 3 + \log _ { 2 } ( x + 1 )$, giving your answer correct to 3 significant figures.\\

\hfill \mbox{\textit{CAIE P3 2017 Q2 [5]}}