Question 970075
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.


{{{graph(300,200,0,6,-1,20,(1/3)*(lne^(3x))-(3e^(lnx))-12)}}}