| Exam Board | CAIE |
|---|---|
| Module | P3 (Pure Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Solve ln equation using subtraction law |
| Difficulty | Moderate -0.5 This is a straightforward application of logarithm laws requiring students to use the subtraction law to combine logs, convert to exponential form, and solve a linear equation. It's slightly easier than average as it follows a standard template with no complications, though it does require multiple steps and careful algebraic manipulation. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| \(2 = \log_{10} 100\) | M1 | |
| Remove logarithms and obtain \(x + 9 = 100x\), or equivalent | A1 | |
| Obtain answer \(x = \frac{9}{11}\) | A1 | 3 marks |
$2 = \log_{10} 100$ | M1 |
Remove logarithms and obtain $x + 9 = 100x$, or equivalent | A1 |
Obtain answer $x = \frac{9}{11}$ | A1 | 3 marks1 Solve the equation $\log _ { 10 } ( x + 9 ) = 2 + \log _ { 10 } x$.
\hfill \mbox{\textit{CAIE P3 2014 Q1 [3]}}