| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2010 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Solve log equation reducing to quadratic |
| Difficulty | Standard +0.8 Part (a) requires careful algebraic manipulation (squaring twice, checking for extraneous solutions). Part (b) involves non-standard log base manipulation with fractional coefficients and requires consolidating multiple log terms before solving. While both are systematic, they demand more careful execution than typical A-level questions and the AEA context indicates above-average difficulty, though neither requires particularly novel insight. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.06d Natural logarithm: ln(x) function and properties1.06f Laws of logarithms: addition, subtraction, power rules |
1.(a)Solve the equation
$$\sqrt { } ( 3 x + 16 ) = 3 + \sqrt { } ( x + 1 )$$
(b)Solve the equation
$$\log _ { 3 } ( x - 7 ) - \frac { 1 } { 2 } \log _ { 3 } x = 1 - \log _ { 3 } 2$$
\hfill \mbox{\textit{Edexcel AEA 2010 Q1 [12]}}