SOLUTION: how to solve this equation: 3(ln2x)^3-4(ln2x)^2-5ln2x+2=0

Algebra.Com
Question 487617: how to solve this equation:

3(ln2x)^3-4(ln2x)^2-5ln2x+2=0
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113)   (Show Source): You can put this solution on YOUR website!
Let ln(x) = y.

3y^3 - 4y^2 - 5y + 2 = 0
(y - 2)(3y - 1)(y + 1) = 0

y = 2, y = 1/3, or y = -1

ln(x) cannot be negative, eliminating the last case.

ln(x) = 2 ----> x = e^2
ln(x) = 1/3 ----> x = 1/(e^3)
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

            @ThePenguin solved the problem incorrectly, by incorrectly presenting the second solution and by loosing the third solution.

            I came to bring a correct version. 


Let ln(x) = y.


3y^3 - 4y^2 - 5y + 2 = 0
(y - 2)(3y - 1)(y + 1) = 0


y = 2, y = 1/3, or y = -1



        Consider all three cases separately. 



1)  ln(x) = 2    ---->  x = e^2.


2)  ln(x) = 1/3 ---->  x = e^(1/3) = .

3)  ln(x) = -1  ---->  x = e^(-1) = 1/e.

Solved (correctly).



RELATED QUESTIONS

3... (answered by robertb)
solve for x :... (answered by jsmallt9)
just wanna see how these problems are worked out. 1.logc 3sq root y^3 z^2/x^4. sorry... (answered by solver91311)
solve the logarithmic equation symbolically.... (answered by jpg7n16)
Can you help me solve this problem?... (answered by jsmallt9)
rewrite as a single logarithm: 2ln4x+ln2x-ln5x Solve:... (answered by nerdybill)
ln2x-ln(x-2)=ln3 what does x... (answered by dabanfield)
can someone help me solve the equation e^2lnx +3e^ln2x... is it the same as x2+2x^3 and... (answered by Alan3354,solver91311)
can someone help me solve e^(ln2x+2ln3x)+e^ln3 n does ln(e^x*e^2)... (answered by Alan3354)