CAIE P3 2012 June — Question 2 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2012
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using power law
DifficultyModerate -0.3 This is a straightforward logarithm equation requiring application of standard log laws (power law and addition law) to simplify, then solving the resulting quadratic. It's slightly easier than average as it follows a standard template with no conceptual surprises, though it does require multiple steps and careful algebraic manipulation.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b

2 Solve the equation \(\ln ( 2 x + 3 ) = 2 \ln x + \ln 3\), giving your answer correct to 3 significant figures.

AnswerMarks Guidance
Use law of the logarithm of a power and a product or quotient and remove logarithmsM1
Obtain a correct equation in any form, e.g. \(\frac{2x+3}{x} = 3\)A1
Solve 3-term quadratic obtaining at least one rootM1
Obtain final answer 1.39 onlyA1 [4]
Use law of the logarithm of a power and a product or quotient and remove logarithms | M1 |
Obtain a correct equation in any form, e.g. $\frac{2x+3}{x} = 3$ | A1 |
Solve 3-term quadratic obtaining at least one root | M1 |
Obtain final answer 1.39 only | A1 | [4]

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2 Solve the equation $\ln ( 2 x + 3 ) = 2 \ln x + \ln 3$, giving your answer correct to 3 significant figures.

\hfill \mbox{\textit{CAIE P3 2012 Q2 [4]}}