Solve for the unknown log5 v+log(1/3) 9+log9 81 = - 4.

We'll identify v as the unknown that has to be
found.

We'll isolate the unknown to the left side and we'll
move the rest of the terms to the right side:

log5 v = -4 -
log9 81 - log(1/3) 9

We'll apply the power rule of
logarithms for the term:

log9 81 = log9 (9^2) = 2log9 9 =
2

We'll change the base of the term log(1/3)
9

log(1/3) 9 = 1/log9
(1/3)

log3 (1/3) = log9 (1/3)*log3
9

log9 (1/3) = log3 (1/3)/log3
9

We'll re-write the numerator and
denominator:

log3 (1/3)= log3 (3^-1) =
-1

log3 9 = log3 (3^2) =
2

log9 (1/3) = -1/2

log5 v =
-4 - 2 - 1/(-1/2)

log5 v = -4 - 2 +
2

We'll eliminate like
terms:

log5 v = -4

W'll take
antilogarithms and we'll get:

v =
5^-4

v = 1/5^4

v
= 1/625