Standard +0.3 This is a straightforward logarithm equation requiring application of standard log laws (power law, subtraction law) to simplify the right side, then exponentiating and solving the resulting quadratic. It's slightly above average difficulty due to requiring multiple steps and algebraic manipulation, but follows a standard template with no novel insight needed.
Use law of the logarithm of a power, quotient or product
M1
Must be used correctly on a correct term. e.g. M1 for \(2\ln x = \ln x^2\) but M0 for \(2\ln x - \ln 2 = 2\ln \frac{x}{2}\). M0 for \(\ln(2x^2-3) = \ln 2x^2 - \ln 3 = \ln 2 + 2\ln x - \ln 3\)
Remove logarithms and obtain a correct equation in \(x\)
A1
e.g. \(2x^2 - 3 = \frac{x^2}{2}\)
Obtain final answer \(x = \sqrt{2}\) only
A1
If \(x = -\sqrt{2}\) is mentioned, it must be rejected
Total: 3
## Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| Use law of the logarithm of a power, quotient or product | M1 | Must be used correctly on a **correct** term. e.g. M1 for $2\ln x = \ln x^2$ but M0 for $2\ln x - \ln 2 = 2\ln \frac{x}{2}$. M0 for $\ln(2x^2-3) = \ln 2x^2 - \ln 3 = \ln 2 + 2\ln x - \ln 3$ |
| Remove logarithms and obtain a correct equation in $x$ | A1 | e.g. $2x^2 - 3 = \frac{x^2}{2}$ |
| Obtain final answer $x = \sqrt{2}$ only | A1 | If $x = -\sqrt{2}$ is mentioned, it must be rejected |
| **Total: 3** | | |
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