Easy -1.2 This is a straightforward logarithm manipulation question requiring only two steps: take logarithms of both sides and rearrange. It's a standard textbook exercise testing basic log laws with no problem-solving element, making it easier than average for A-level.
\([n =] \frac{\log p - \log s}{\log t}\) or \(\frac{\log\left(\frac{p}{s}\right)}{\log t}\) [base not required]
A1
or A2 for \([n =]\log_t\left(\frac{p}{s}\right)\) [base t needed] following first M1; as final answer (i.e. penalise further incorrect simplification)
$\log p = \log s + \log t^n$ | M1 | or $\frac{p}{s} = t^n$
$\log p = \log s + n \log t$ | M1 | $n \log t = \log\left(\frac{p}{s}\right)$
$[n =] \frac{\log p - \log s}{\log t}$ or $\frac{\log\left(\frac{p}{s}\right)}{\log t}$ [base not required] | A1 | or A2 for $[n =]\log_t\left(\frac{p}{s}\right)$ [base t needed] following first M1; as final answer (i.e. penalise further incorrect simplification)