| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Simultaneous equations with logarithms |
| Difficulty | Standard +0.3 This is a straightforward simultaneous equations problem requiring substitution and basic logarithm laws (sum rule). The steps are clear: substitute a=3b into the log equation, apply log₃(3b·b)=2, simplify to get b²=3, then find both values. Slightly above average difficulty due to combining algebraic manipulation with logarithms, but follows standard C2 techniques without requiring novel insight. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.06f Laws of logarithms: addition, subtraction, power rules |
Given that $a$ and $b$ are positive constants, solve the simultaneous equations
$a = 3b$,
$\log_3 a + \log_3 b = 2$.
Give your answers as exact numbers.
[6]
\hfill \mbox{\textit{Edexcel C2 Q5 [6]}}