No, no... you are making it far too complicated.
What is [tex]I_X[/tex] in terms of [tex]I_E[/tex] ? In other words, what number do you have to multiply [tex]I_E[/tex] by to get [tex]I_X[/tex]?
Then get rid of [tex]I_X[/tex] in your equation.
Finally think about what multiplication inside of a log function maps to on the outside. I'll give you a clue on the last one and it is +.