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

 +  = 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 = .

 ------ 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