Moderate -0.5 This is a straightforward application of the logarithm subtraction law (ln a - ln b = ln(a/b)) followed by exponentiating both sides. It requires only two standard steps with no conceptual difficulty, making it slightly easier than average but not trivial since students must recognize the structure and manipulate correctly.
Apply at least one logarithm law for product or quotient correctly (or exponential equivalent)
M1
Obtain \(x + 5 = ex\) or equivalent and hence \(\frac{5}{e-1}\)
A1
[3]
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| State or imply $\ln e = 1$ | B1 | |
| Apply at least one logarithm law for product or quotient correctly (or exponential equivalent) | M1 | |
| Obtain $x + 5 = ex$ or equivalent and hence $\frac{5}{e-1}$ | A1 | [3] |
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