How Do You Solve the PCM System Quantization Problem from Leon Couch's Book?

[Domenico94]

Homework Statement

Hi everyone. I was trying to solve an exercise from the book Leon couch, communication systems, number 3.7 of the 6th edition. This is the statement:
In a PCM binary system, the quantisation noise mustn t exceed the percentage value P of the peak power. Show that the required number of bit for each word is:

N> log2(10)*log(50/P).

I tried to solve it by applying this reasoning :
The s/n ratio is equal to 3M^2 for a PCM system. Then
If N<(p/100)*s, then s/n>(100/p). Then I solve it by passing to decibel, and making the logaritm, but I obtain something quite different, and I don t undestand where I was wrong.

 

[Domenico94]

Anyone??