SOLUTION: {{{ (log ( 3, x ))^2 - log (3, x ) = 3 }}}

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Question 748069: +%28log+%28+3%2C+x+%29%29%5E2+-+log+%283%2C+x+%29+=+3+
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
%28log%283%2C%28x%29%29%29%5E2-log%283%2C%28x%29%29=3
let+u=log%283%2C%28x%29%29
u%5E2=%28log%283%2C%28x%29%29%29%5E2
u^2-u-3=0
solve by quadratic formula:
u≈-1.303 (reject, log>0)
u≈2.303=log%283%2C%28x%29%29
x=3^2.303≈12.51
..
Check:
%28log%283%2C%28x%29%29%29%5E2-log%283%2C%28x%29%29=(2.30)^2-2.30≈3