CAIE P3 2016 March — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionMarch
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using power law
DifficultyStandard +0.3 This is a straightforward logarithm equation requiring application of standard log laws (power law and addition law) to simplify, then solving a quadratic equation. While it requires multiple steps, the techniques are routine for A-level and the algebraic manipulation is standard, making it slightly easier than average.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b
1 Solve the equation \(\ln \left( x ^ { 2 } + 4 \right) = 2 \ln x + \ln 4\), giving your answer in an exact form.
AnswerMarks Guidance
Remove logarithms and obtain a correct equation in \(x\), e.g. \(x^2 + 4 = 4x^2\)M1
Obtain final answer \(x = 2/\sqrt{3}\), or exact equivalentA1 [3] 
Remove logarithms and obtain a correct equation in $x$, e.g. $x^2 + 4 = 4x^2$ | M1 |
Obtain final answer $x = 2/\sqrt{3}$, or exact equivalent | A1 | [3]
1 Solve the equation $\ln \left( x ^ { 2 } + 4 \right) = 2 \ln x + \ln 4$, giving your answer in an exact form.

\hfill \mbox{\textit{CAIE P3 2016 Q1 [3]}}
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