1.7: An arithmetic series of logarithms

4PM1/1R/November/2020 — Question 3 · 7 marks

The n\displaystyle nth term of an arithmetic series is un\displaystyle u_n such that
un=ln a+(n−1)ln b,u_n=\mathrm{ln}\,a+(n-1)\mathrm{ln}\,b,
where a\displaystyle a and b\displaystyle b are positive integers.
Given that u2=ln 12\displaystyle u_2=\mathrm{ln}\,12 and that u5=ln 768\displaystyle u_5=\mathrm{ln}\,768, find the value of a\displaystyle a and the value of b\displaystyle b.
(7)