Moderate -0.3 This is a straightforward logarithm equation requiring application of standard log laws (sum and power rules) to form a quadratic equation. While it involves multiple steps and algebraic manipulation, it follows a predictable pattern with no conceptual surprises, making it slightly easier than average for A-level.
Use law of logarithm of a power and sum, remove logarithms
M1
Obtain correct equation e.g. \(3(2x+5)=(x+2)^2\)
A1
Use correct method to solve a 3-term quadratic, obtaining at least one root
M1
Obtain final answer \(x = 1+2\sqrt{3}\) or \(1+\sqrt{12}\) only
A1
## Question 2:
| Use law of logarithm of a power and sum, remove logarithms | M1 | |
| Obtain correct equation e.g. $3(2x+5)=(x+2)^2$ | A1 | |
| Use correct method to solve a 3-term quadratic, obtaining at least one root | M1 | |
| Obtain final answer $x = 1+2\sqrt{3}$ or $1+\sqrt{12}$ only | A1 | |
---