My problem is 2^3x=3^x+4

i have been trying this problem and have done or gotten this far.. i dont know if its right or wrong but....

3x ln2= x+4 ln3

3 ln2 + x ln2 = x ln 3 + 4 ln 3

x ln 2 - x ln 3 = 4 ln 3 - 3 ln 2

x ln 2/3 = ? ln 3/2

this is what i got and im stumped am i on the right track and or what is the next step..

any help is appreciated