1.33: Solve the equation Give your answer in the form where is prime and is an integer.

4PM1/2R/June/2025 — Question 9 · 9 marks

(i) Solve the equation 3(loga9+loga27)=1\displaystyle 3(\mathrm{log}_a 9 + \mathrm{log}_a 27) = 1
Give your answer in the form a=bc\displaystyle a = b^c where b\displaystyle b is prime and c\displaystyle c is an integer.
(3)
(ii) Solve the equation log4p+logp256=−4\displaystyle \mathrm{log}_4 p + \mathrm{log}_p 256 = -4
(6)