Find a function of the form $\displaystyle y=ax^b lnx$ where a and b are nonzero constants and a local max at $\displaystyle (e^2, 6e^-1)$

So I'm not sure where to start on this one. I'm not too sure what all the different families of curves are, I found this website:Exponential and Logarithmic Function Gallery

but I can't tell which one of those my equation fits into.

Can I get some advice of where to start?