Question

IEEE 754 - Little questions here and there for a problem that has solutions included:
http://i.imgur.com/6eAJf47.jpg

Answer 1

1) What is the reasoning behind the log(-8.573 × 10^13) / log(2) computation?

2) When obtaining the exponent 47 in 2^47 from the computation in my question #1, I noticed that a 2^47 / 1.4074 × 10^14 = 1 was multiplied with -8.573 × 10^13.

My question for this part #2 is: why was that 47 “hunted down”? Why couldn't I have multiplied -8.573 × 10^13 by 2^50 / 1.1259 × 10^15 = 1 for example? Is there a significance to this or could I have chosen to multiply by 2^46 / 7.034 × 10^13 as well?

3) For the number of significant bits, I get the 14 – 1 part but, I don't understand how the 4/log(2) computation was obtained.

If something is unclear with what I am asking, tell me and I will attempt to clarify the situation.

Any input would be greatly appreciated!