How do I write a log likelihood function when I have 2 mean values for my pdf? I have been given the following pdf :
fT (t; B, C) = ( exp(-t/C) - exp(-t/B) ) / ( C - B )  ,  (t>0)
where the overall mean is B+C.
I am unsure as to how to write the log likelihood function of B and C.
The next part of the Q asks me to derive the equations that would have to be solved in order to find the max likelihood estimators of B and C.
I would be grateful for any help =)

By definition, the log-likelihood is given by
$$
\ln \mathcal{L}(B,C|x_1 , \ldots ,x_n ) = \sum\limits_{i = 1}^n {\ln f(x_i|B,C)}.
$$
Thus, in our example, 
$$
\ln \mathcal{L}(B,C|x_1 , \ldots ,x_n ) = \sum\limits_{i = 1}^n {\ln \bigg[\frac{{e^{ - x_i /C}  - e^{ - x_i /B} }}{{C - B}}\bigg]} .
$$
EDIT: In view of the next part of the question, it may be useful to write
$$
\ln \mathcal{L}(B,C|x_1 , \ldots ,x_n ) = \sum\limits_{i = 1}^n {\ln [e^{ - x_i /C}  - e^{ - x_i /B} ]}  - n\ln (C - B).
$$
