SOLUTION: What is (log3 x)^2 = log3 x^2 + 3. The answer in the answers part is 27 and 1/3. Thank you.

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Question 2882: What is (log3 x)^2 = log3 x^2 + 3.
The answer in the answers part is 27 and 1/3.
Thank you.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Since log3 x^2 = 2 log3 x,
(log3 x)^2 = log3 x^2 + 3 converts to
(log3 x)^2 - 2log3 x - 3 = 0.
Let u = log3 x, we have u^2 - 2u -3 =0,
Factoring (u-3)(u+1) =0,
So, u =3 or -1.
Hence, log3 x = 3,u = 3^3 = 27 or
log3 x = -1,u = 3^(-1) = 1/3