What is x for log 3 9 - log 3 2 = log 3 x?

For the logarithm to exist, x has to be
positive.

log 3 (x) = log 3 (3)^2 - log 3
(2)

Because the bases are matching, we'll transform the
difference of logarithms from the right side, into a quotient. We'll apply the
formula:

lg a - lg b = lg
(a/b)

We'll substitute a by 9 and b by 2. The logarithms
from formula are decimal logarithms. We notice that the base of logarithm is
3.

log 3 (x) = log 3
(9/2)

Because the bases are matching, we'll apply the one
to one property:

x =
9/2

x =
4.5

Since the value of x is positive, the
solution of the equation is valid.