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I don't understand the contents in Sybex, CWNA, 2009

p.70&71, chapter 3, about dB

AP transmit data at 100mW. Laptop1 receives signal at power level of 10mW. Laptop2 receives signal at power level of 1mW.

The signal difference between AP (100mW) to Laptop1 (10mW) is 100:10, or 1 bel (This point is clear).
The signal difference between Laptop1 (10mW) to Laptop2 (1mW) is 10:1, or 1 bel, so the power difference between the AP and Laptop2 is 2 bel. (I don't understand why this is 2??, Why not 100:1?)

And so, power ratios is following:
AP:Laptop1:Laptop2 = 100:10:1
Diffrence between AP and Laptop2:
AP:Laptop2 = 100:1 or 2 bel.

By using formula,
bels = log(P1/P2)
bels = log(100/1)
thus bels = 2
(I got it)
However, is the errata on page 71??
A decibel is equal to one-tenth of a bel... << correct!
bels = log (P1/P2)
decibels = 10 x log (P1/P2) << Question here? why not: decibels = 1/10 x log (P1/P2)

10 x log (P1/P2) is correct.
the end-result of the initial calculation will be the same (in this example "2" when using 100 and 1 and showing in bel), however if you want the result to be shown in decibel you will need to multiply it with 10.. 20 decibel are 2 bel and this won't change the end-result..

edit: it's like saying 1000 gram are 1 kilo.. it's eventually the same weight, but the gram need to be multiplied by 1000, not divided :)

James,

Are you in the Telephone Industry?
I haven't seen anything other than historical references to Bels, since I worked on a phone system back in the 80's.

Decibels, milliwatts, dB microvolts, or dB, dBm, mw, and dBmV are the only thing I see any more. To be honest, I don't even talk about Bels anymore, and try not to talk about dBmV, except when my RF Compliance friends insist.