Given that logₐp + logₐ5 - logₐ4 = logₐ20, find the value of p.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [1] B1 for logₐ(5p/4) = logₐ20 oe
2. [1] B1 for 16, nfww
3. [1] M1 For recognition of a correct quadratic in 3^x and attempt to factorise or use quadratic formula
4. [1] M1 dep for a correct attempt to solve 3^x = k, k > 0
5. [1] A1 for one solution only, must be from a correct solution.
6. [1] B1 May be implied by e.g. logᵧ2 = 1/log₂y or 1/log₂y
7. [1] M1 For obtaining a 3 term quadratic equation in either logᵧ2 or log₂y and solving to obtain logᵧ2 = k or log₂y = k, may be implied or equivalent using an alternative base.
8. [1] A1 nfww