| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Session | Specimen |
| Marks | 3 |
| Topic | Laws of Logarithms |
| Type | State value of basic log |
| Difficulty | Moderate -0.8 This is a straightforward logarithm question requiring basic index manipulation (converting to base 2) and direct application of log definition. Part (i) is routine equation solving with powers, and part (ii) is immediate recall once x is found. Simpler than average A-level as it involves no problem-solving insight, just mechanical application of standard techniques. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06g Equations with exponentials: solve a^x = b |
(i) Express equation as $2^{12x} = 2^{6x-12}$ [M1]
Obtain $x = -2$ [A1] **2 marks**
(ii) $\log_4 2 = 0.5$ or $\frac{1}{2}$ [B1] **1 mark**1 It is given that $8 ^ { 4 x } = 4 ^ { 3 x - 6 }$.\\
(i) By expressing each side as a power of 2 , find the value of $x$.\\
(ii) Write down the value of $\log _ { 4 } | x |$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 Q1 [3]}}