CAIE P3 2016 June — Question 1 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyModerate -0.8 This is a straightforward exponential equation requiring taking logarithms of both sides and rearranging to isolate x. It's a standard textbook exercise with a clear method (take logs, use log laws, collect x terms, solve) requiring no problem-solving insight, making it easier than average but not trivial since it involves algebraic manipulation with logarithms.
Spec1.06g Equations with exponentials: solve a^x = b

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

AnswerMarks Guidance
Use law of the logarithm of a product, power or quotientM1*
Obtain a correct linear equation, e.g. \((3x - 1)\ln 4 = \ln 3 + x \ln 5\)A1
Solve a linear equation for \(x\)DM1*
Obtain answer \(x = 0.975\)A1 [4]
Use law of the logarithm of a product, power or quotient | M1* |
Obtain a correct linear equation, e.g. $(3x - 1)\ln 4 = \ln 3 + x \ln 5$ | A1 |
Solve a linear equation for $x$ | DM1* |
Obtain answer $x = 0.975$ | A1 | [4]
1 Use logarithms to solve the equation $4 ^ { 3 x - 1 } = 3 \left( 5 ^ { x } \right)$, giving your answer correct to 3 decimal places.

\hfill \mbox{\textit{CAIE P3 2016 Q1 [4]}}