How do I answer these questions?

Question1:

Using examples, explain where you would want to use the linear, power law and logarithmic transforms

Question2:

When is histogram equalization useful? When might it fail? Provide an example.

Question3:

Assume you have an image with some unknown contrast that you wish to normalize and dont care about the brightness. Derive a point operator that stretches contrast so that =0 and =, where =255 for 8-bit images and =1 for floating-point images.

Question4:

When would it not be appropriate to use a LUT?

Question 5:

If an image is stored with 8-bpc, then what is the advantage of processing with a higher bit-depth? Why might we want to use floating-point values?