SOLUTION: Find the integer k, k > 2, for, which log (k - 2)! + log(k - 1)! + 2 = 2 log k!.

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Question 530282: Find the integer k, k > 2, for, which log (k - 2)! + log(k - 1)! + 2 = 2 log k!.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
I presume that the factorial is inside the log, otherwise it would not easily be defined.

We can write the original equation,

, as

, using logarithmic properties.





, upon simplifying the factorial expression in the LHS. Assuming the log is in base 10,

, in which k = 5 is the unique positive integer solution.