[R] Fitting linear model to the matrix

[Huhrik Beybutov]

I'm afraid I need your help with linear models in R, I apologize in
advance is this question was beaten to death.

I'm trying to fit Y( i, j ), where i is row, j is column. My model is
log [ Y( i, j ) ] = log A( i ) * B( j )+ C( i ) ]  + error.  I have i
x j  observations, I need to find 2*i + j parameters.

What would be the best way to approach this? 

Thank you!

- H.