Since we have the term log3 x^2, we'll use the power property of
logarithms:log3 x^2 = 2 log3 x.
The given equation (log3 x)^2 = log3
x^2 + 3 converts to
(log3 x)^2 - 2log3 x - 3 =
0
We'll substitute log3 x = u.
We'll
re-write the equation:
u^2 - 2u -3
=0
Factoring, we'll get:
(u-3)(u+1)
=0
We'll put each factor as zero:
u-3 =
0
So, u = 3
u + 1 =
0
u = -1
But log3 x = 3 => x =
3^3 => x = 27
log3 x = -1
=> x = 3^-1 => x =
1/3
Since both solutions are positive,
we'll accept them.
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