Hi everyone,

This is my first post, so please bear with me if I am posting in the wrong forum.

I study economics and I am reading an article. I do not understand how the author gets the following conclusions:

He takes log of this function:

And ends up with:

I thought it would be instead of the log[T!/(T-t)].

Secondly I want do differentiate logc_t^t, but I am unsure how to deal with the log sum expressions. How do you differentiate ??

Wolfram alpha uses gamma functions which I honestly do not understand. The article I am reading finds the following derivative:

I hope someone can clearify this for me. Thank you very much!

Jacob