For the logarithm to exist, x has to be
positive.
We'll write 2
as:
2*1 = 2* log 3 3
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)
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
admissible.
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