What is the role of Log-sum-exp?

[navidstuv]

In your code for defining Loss function, you firstly take the log of distributions then add them up, whereas the loss mentioned in Bishop is log of sum of distribution.I am confused, Maybe there is something in trick you used for log-sum-exp.
Can you please formulate this?

[edmondja]

not to have a too big exponent he substracts the max