SOLUTION: Solve for x. ((1/3)ln e^(3x)-3e^(ln x)=12. The answer is no solution but I'm not sure how to prove that it has no solution. Please help. Thank you.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve for x. ((1/3)ln e^(3x)-3e^(ln x)=12. The answer is no solution but I'm not sure how to prove that it has no solution. Please help. Thank you.       Log On


   

Question 970068: Solve for x. ((1/3)ln e^(3x)-3e^(ln x)=12. The answer is no solution but I'm not sure how to prove that it has no solution. Please help. Thank you.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28x%29 and e%5E%28x%29 are inverse functions.
ln%28e%5Ex%29=x
e%5E%28ln%28x%29%29=x
So,
%281%2F3%29%283x%29-3x=12
x-3x=12
-2x=12
x=-6
However x=-6 is not allowed since ln%28-6%29 is not defined.
There is no solution.