Moderate -0.8 This is a straightforward exponential equation requiring a standard technique: take logarithms of both sides, apply log laws, and solve the resulting linear equation. It's routine A-level work with no conceptual challenges, making it easier than average, though not trivial since it requires careful algebraic manipulation.
Obtain a correct linear equation in \(x\), e.g. \((3-2x)\ln 5 = \ln 4 + x\ln 7\)
A1
Obtain answer \(x = 0.666\)
A1
Total
4
**Question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Use law of the logarithm of a product or quotient | M1 | |
| Use law of the logarithm of power **twice** | M1 | |
| Obtain a correct linear equation in $x$, e.g. $(3-2x)\ln 5 = \ln 4 + x\ln 7$ | A1 | |
| Obtain answer $x = 0.666$ | A1 | |
| **Total** | **4** | |
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