Moderate -0.5 This is a straightforward application of logarithm laws (subtraction and power rules) leading to a simple linear equation. It requires only routine manipulation: ln((x+1)/x) = ln(4), then (x+1)/x = 4, solving to x = 1/3. Slightly easier than average due to minimal steps and standard technique.
Use correct logarithm property to produce one term on LHS
M1
Use correct process to obtain equation without logarithms
M1
Obtain \(\frac{x+1}{x} = 4\) or equivalent and hence \(x = \frac{1}{3}\)
A1
Total
3
**Question 1:**
| Answer | Mark | Guidance |
|--------|------|----------|
| Use correct logarithm property to produce one term on LHS | M1 | |
| Use correct process to obtain equation without logarithms | M1 | |
| Obtain $\frac{x+1}{x} = 4$ or equivalent and hence $x = \frac{1}{3}$ | A1 | |
| **Total** | **3** | |
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