SPS SPS SM Pure 2021 May — Question 3 6 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2021
SessionMay
Marks6
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyStandard +0.3 This is a straightforward exponential equation requiring taking logarithms of both sides and rearranging algebraically. The method is standard (take log₁₀ of both sides, use log laws, collect x terms, factorize) and commonly practiced. While it requires careful algebraic manipulation across 6 marks, it involves no conceptual difficulty or novel insight—just systematic application of logarithm rules.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b

Solve the equation \(2^{4x-1} = 3^{5-2x}\), giving your answer in the form \(x = \frac{\log_{10} a}{\log_{10} b}\). [6]

Solve the equation $2^{4x-1} = 3^{5-2x}$, giving your answer in the form $x = \frac{\log_{10} a}{\log_{10} b}$. [6]

\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q3 [6]}}