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Loss function for non-linear model fit

I've been beating my head on this one, with not too much success.
I'm trying to build the maximum likelihood loss functions for two equations, where lambda (and lambdas/m) are parameters, and N and x are column values, and s and pi are constants.
(N*s*pi)*lambda*exp(-lambda*x)
and
(N*s*pi)*(p*lambdas*exp(-lambdas*x)+(1-p)*lambdam*exp(-lambdam*x))
Any suggestions?
thanks so much.