Log 384/5 + log 81/32 + 3log 5/3 + log 1/3
using the properties of logs, and assuming base 10, this is
log(384/5 * 81/32 * (5/3)^3 * 1/3) = log300 = 2+log3
or,
7log2+log3-log5+4log3-5log2+3log5-3log3-log3
= 2log2+log3+2log5
= 2log(2*5)+log3
= 2log10+log3
= 2+log3
Also, this solution can be written as a single logarithm.
Since for logarithms base 10:
log 100 = 2
and
log ( a • b ) = log a + log b
2 + log 3 = log 100 + log 3 =
log ( 100 • 3 ) = log 300