CAIE P2 2011 November — Question 2 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2011
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyModerate -0.8 This is a straightforward exponential equation requiring a standard technique: take logarithms of both sides, apply log laws to bring down the exponents, then solve the resulting linear equation. It's a routine textbook exercise with a single clear method and no conceptual challenges, making it easier than average but not trivial since it requires correct application of logarithm properties.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b

2 Use logarithms to solve the equation \(4 ^ { x + 1 } = 5 ^ { 2 x - 3 }\), giving your answer correct to 3 significant figures.

AnswerMarks Guidance
Use law for the logarithm of a product, a quotient or a powerM1*
Obtain \((x + 1)\log 4 = (2x - 3)\log 5\), or equivalentA1
Solve for \(x\)M1(dep*)
Obtain answer \(x = 3.39\)A1 [4]
Use law for the logarithm of a product, a quotient or a power | M1* |
Obtain $(x + 1)\log 4 = (2x - 3)\log 5$, or equivalent | A1 |
Solve for $x$ | M1(dep*) |
Obtain answer $x = 3.39$ | A1 | [4] |
2 Use logarithms to solve the equation $4 ^ { x + 1 } = 5 ^ { 2 x - 3 }$, giving your answer correct to 3 significant figures.

\hfill \mbox{\textit{CAIE P2 2011 Q2 [4]}}