I'm having trouble rearranging the following equation to make $x$ the subject; $$ y = e^{\frac{t}{\sqrt[3]{x}}} + x$$ This equation is one formula used to calculate distance ($x$) between an extraction hood and an industrial process. Currently I have to use trial and error if I want to create a system that is effective over a specific distance as I cannot make x the subject. If x was the subject then I could specify the distance and then create the system based on that.
I have tried using natural logs to remove x as the power but I am just left with $\ln x$ which I then cannot reduce.
I'm sure it must be possible but I cannot for the life of me figure it out. Any help would be much appreciated!
