I don't see a question here! What is the question?
Also what does "log^18" mean? I that just log(18)? And is that common log (base 10) or natural log (base e)? Or is the problem to find base a such that loga(18)- loga(10)= 19?
If that is the case, you can simplify by using the fact that loga(18)- loga(10)= loga(18/10)= loga(9/5) and then you are trying to find a such that a19= 9/5.