Hello JbuckhamI think it's a simple case of not interpreting the notation correctly.
You have interpreted to mean . But I think that, in this question, is function notation, and means , expressed as a function of , is equal to ...
So the equation you're being asked to solve is simply:
(Why do people make life more difficult than it needs to be, eh?)
Grandad
Oh, I thought when you wrote that you were specifying as a function of . Instead, we have
which has no solutions. You can see from their graphs: the exponential function starts out at much higher values than the linear function, and then it begins to grow at such a quickly increasing rate that the linear function can never hope to catch up.
Edit: Grandad may be right--perhaps you have misinterpreted the problem? You may want to state the question exactly as it is written in your book or assignment.