CAIE P2 2010 November — Question 2 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2010
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, and solve the resulting linear equation. It's simpler than average A-level questions as it's purely procedural with no problem-solving element, though not trivial since students must correctly manipulate logarithms.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b

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

AnswerMarks Guidance
Use law for the logarithm of a product, a quotient or a powerM1*
Obtain \(x\log 5 = (2x+1)\log 2\), or equivalentA1
Solve for \(x\), via correct manipulative technique(s)M1(dep*)
Obtain answer \(x = 3.11\). Allow \(x \in [3.10, 3.11]\)A1 [4]
Use law for the logarithm of a product, a quotient or a power | M1* |

Obtain $x\log 5 = (2x+1)\log 2$, or equivalent | A1 |

Solve for $x$, via correct manipulative technique(s) | M1(dep*) |

Obtain answer $x = 3.11$. Allow $x \in [3.10, 3.11]$ | A1 | [4]
2 Use logarithms to solve the equation $5 ^ { x } = 2 ^ { 2 x + 1 }$, giving your answer correct to 3 significant figures.

\hfill \mbox{\textit{CAIE P2 2010 Q2 [4]}}