Question

Log 384/5 + log 81/32 + 3log 5/3 + log 1/3

Answer 1

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

Answer 2

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