How to calculate weighted negative log-likelihood?

Hello

I'm calculating the negative log-likelihood for a bunch of tasks:

NLL = p1∗p2∗...∗pn = −(log(p1)+...+log(pn))

p is the probability of a task. The tasks appear at a certain time point and I want to give to the newer tasks a higher weight (influence).

If I have weights for each task (i.e. n weights), how can I calculate the weighted NLL?