Where to input a log expression in FFMPEG
This is the original expression to be implemented.

x &gt; 0.14996582 ? (pow(10,0, (x - 0.385537) / 0.2471896) - 0.0522720) / 5.5555556 : (x - 0.092809) / 5.367655


where x is the pixel intensity normalized to [0,1]. x is linear, so gamma returns identity. 

I'm going to assume the 0 in the pow expression is an extraneous arg since the linked reference at http://strattoncamera.com/pdf/11-06-30_Alexa_LogC_Curve.pdf depicts pow() as having only two arguments. I'm also assuming that the input is 16-bit full-range integer RGB.

ffmpeg -apply_trc linear -i in%d.exr
       -vf "lutrgb=r='if(gt(val/maxval,0.14996582),maxval*((pow(10, (val/maxval-0.385537)/0.2471896)-0.0522720)/5.5555556),maxval*((val/maxval-0.092809)/5.367655))':
                   g='if(gt(val/maxval,0.14996582),maxval*((pow(10, (val/maxval-0.385537)/0.2471896)-0.0522720)/5.5555556),maxval*((val/maxval-0.092809)/5.367655))':
                   b='if(gt(val/maxval,0.14996582),maxval*((pow(10, (val/maxval-0.385537)/0.2471896)-0.0522720)/5.5555556),maxval*((val/maxval-0.092809)/5.367655))'"
        out%d.tiff