Standard +0.3 This question requires applying logarithm laws (power and subtraction rules) to simplify the equation, then solving a resulting quadratic. It's slightly above average difficulty due to the algebraic manipulation needed after applying log laws, but remains a standard textbook exercise with clear steps and no novel insight required.
Use law for the logarithm of a product, quotient or power
M1
Remove logarithms and state a correct equation, e.g. \(x(2x-1) = (x+1)^2\)
A1
Solve a 3-term quadratic obtaining at least one root
M1
Obtain answer \(3.303\) only
A1
Total
4
**Question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Use law for the logarithm of a product, quotient or power | M1 | |
| Remove logarithms and state a correct equation, e.g. $x(2x-1) = (x+1)^2$ | A1 | |
| Solve a 3-term quadratic obtaining at least one root | M1 | |
| Obtain answer $3.303$ only | A1 | |
| **Total** | **4** | |