Solve for x : log 3 9 - log 3 2 = log 3 x .

We'll impose one constraints for the logarithm log 3 x to
exist.

x > 0

We'll use
the power property of logarithms:

log 3 9 = 2* log 3 3 =
2

We'll use the power property of logarithms and the
symmetric property:

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)

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

x = 9/2

x =
4.5

Since the value of x >0, we'll
validate x = 4.5 as the solution of the equation.