| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | May |
| Marks | 6 |
| Topic | Exponential Equations & Modelling |
| Type | Simple exponential equation solving |
| Difficulty | Standard +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. |
| Spec | 1.06f 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]
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q3 [6]}}