1.5^11 = -1.5^n+5

Are you trying to solve this:


1.5^{11} = (-1.5)^n + 5


(which is what you wrote) or this:


1.5^{11} = (-1.5)^{n + 5}


For now I will assume the latter. The right hand side can be rewritten to give you:


1.5^{11} \ = \ -1^{(n+5)}\ \times \ 1.5^{(n+5)}


You can see that the value of n+5 = 11. So what is the value for n? But note that the left hand side is a positive number while the right hand side is positive only if
-1 is raised to an even power. Does the value for n that you just found work? What does this tell you about this equation?