# Luminous emittance vs value recorded on image sensor

Assume that I have a light bulb with luminous emittance of 160000lux (16ev), and a gray wall with luminous emittance of 300lux (7ev). I take the photo of this bulb and this background. Is there any approximate formula to estimate the gray level or RGB value of the bulb and the background in the image. In this case, I assume that the exposure is set for the light bulb (so the background should be very dark). Let's say the grayscale is 8 bits. If the gray level of the bulb is 255, what would be the gray level of the wall.

Thanks!