HW Question: Log-Likelihood Function

#1
Attached to this post is my homework from my statistics course along with my own attempt at a solution. (The files are merged together into one PDF)

I need help with problem 1 Part B, which asks me to find the log-likelihood function of the given probability mass function.

The problem I am running into is that when I plot log-likelihood function (actually 2*log-likelihood), I cannot get the desired maximum which represents the MLE. I believe that there is a mistake in my previous calculations, but I cannot find it.

THANKS!
 

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