| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Solve exponential equation by substitution |
| Difficulty | Moderate -0.8 This is a standard C2 exponential equation using substitution to form a quadratic. Part (a) requires routine manipulation of index laws (recognizing 4^x = (2^2)^x = (2^x)^2 and 2^(x+1) = 2·2^x), while part (b) involves solving a straightforward quadratic and taking logarithms. The substitution is explicitly given, making this easier than average with no problem-solving insight required—purely procedural application of well-practiced techniques. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}[label=(\alph*)]
\item Using the substitution $u = 2^x$, show that the equation $4^x - 2^{(x + 1)} - 15 = 0$ can be written in the form $u^2 - 2u - 15 = 0$. [2]
\item Hence solve the equation $4^x - 2^{(x + 1)} - 15 = 0$, giving your answers to 2 decimals places. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q34 [6]}}