Answer:
7log(10/9) = 7(log 10 - log 9)
= 7(log 5 + log 2 - 2 log 3)
2log(25/24) = 2(log 25 - log 24)
= 2(2 log 5 - (log 8 + log 3))
= 2(2 log 5 - 3 log 2 - log 3)
3log(80/81) = 3(log 80 - log 81)
= 3(log 16 + log 5 - 4 log 3)
= 3(4 log 2 + log 5 - 4 log 3)
7log(10/9) - 2log(25/24) - 3log(80/81) =
7 log 5 + 7 log 2 - 14 log 3 - 4 log 5 +
6 log 2 + 2 log 3 - 12 log 2 - 3 log 5 +
12 log 3 = log 2