# Question 4:

## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\log_3 x^2 - \log_3(x+4) = \log_3 \frac{x^2}{x+4}$ | B1* | Obtain $\log_3 x^2 - \log_3(x+4)$. Allow no base. Could be implied if both log steps done together. Allow equiv eg $2(\log_3 x - \log_3(x+4)^{0.5})$ |
| | B1d* | Obtain $\log_3 \frac{x^2}{x+4}$ or equiv single term. CWO so B0 if eg $\frac{\log x^2}{\log(x+4)}$ seen in solution. No ISW if subsequently incorrectly 'simplified' eg $\log_3(\frac{x}{4})$. Must now have correct base in final answer |

## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{x^2}{x+4} = 3^2$ | M1* | Attempt correct method to remove logs. Equation must be of form $\log_3 f(x) = 2$, with $f(x)$ being the result of a legitimate attempt to combine logs. Allow use of their (i) only if it satisfies the above criteria, so $x^2 - (x+4) = 9$ is M0 whether or not in (i) |
| $x^2 = 9(x+4)$ | A1 | Obtain any correct equation. Not involving logs |
| $x^2 - 9x - 36 = 0$ | M1d* | Attempt complete method to solve for $x$. Solving a 3 term quadratic. Must attempt at least one value of $x$ |
| $(x-12)(x+3) = 0$ | | |
| $x = 12$ | A1 | Obtain $x = 12$ as only solution. Must be from a correct solution of a correct quadratic. A0 if other root (if given) is not $x = -3$. A0 if $x = -3$ still present. Not necessary to consider $x = -3$ and then discard, but A0 if discarded for incorrect reason |