SOLUTION: Solve for x. (1/3) lne^(3x)- 3e^(lnx)=12. There is no solution but I don't know how to prove that. Please help. Thank you.

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Question 970075: Solve for x. (1/3) lne^(3x)- 3e^(lnx)=12. There is no solution but I don't know how to prove that. Please help. Thank you.
Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Solve for x. (1/3) lne^(3x)- 3e^(lnx)=12
(1/3)*(3x)- 3x = 12
x - 3x = 12
x = -6
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--> ln of a negative number, not allowed --> no solution

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
ln (e ^ something) = something. ln and e are opposites, like dividing and multiplying.
(1/3) lne^(3x)- 3e^(lnx)=12; e^lnx =1
(1/3)* 3x -3 =12
x -3 =12
x=15
Check this
(1/3) ln e^(45)- 3 e^(ln 15)=12
15-15 =0
but 0 does not equal 12. No solution
Try ln (1)=0; (1/3)* ln e^3-3e(0)=12; (1/3)*3 -0=12, which is not true.