SOLUTION: {{{ (ln x)^2 + 2*(ln x) = 3 }}}

Question 1095952:
Found 3 solutions by KMST, ikleyn, MathTherapy:
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!

and
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
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+ = 3 ====> + + 1 = 4 ====> = 4 ====> ln(x) + 1 = +/- 2 ====> Case a): ln(x) + 1 = 2 ====> ln(x) = 1 ====> x = e. Case b): ln(x) + 1 = -2 ====> ln(x) = -3 ====> x = . Answer. There are two solutions: x = e and x = .

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

------ Replacing 2 ln (x) with 3 ln (x) � ln (x)
ln (x)[ln (x) + 3] � 1 [ln (x) + 3] = 0
[ln (x) � 1][ln (x) + 3] = 0
ln (x) � 1 = 0 OR ln (x) + 3 = 0
ln (x) = 1 OR ln (x) = - 3

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