Log with subscript 2

http://en.wikipedia.org/wiki/Logarithm

Log base 2.

OK, that makes some sense. I've still got problems with this calculation (not the least trying to get it into the calculator). For starters, the text doesn't give any examples at all.

the formula is C = B log (1 + SNR) the log has a subscript of 2.



I don't know what the 400000 in brackets means. And since our instructor hasn't answered one question on our subject forum in 13 weeks, and never answered a question I sent him by email, I see little point in asking him this one.

We're told in the text that telephone equipment allows a bandwidth of 4000Hz with a guardband at each end to prevent interference when voice channels are multiplexed.

Given the info in the wiki link (thanks DrewDad) I'm interpreting the formula for my calculator as

C = B * (log(1+SNR)/log(2))

the bandwidth(B) I assume is the 4000Hz. Is the SNR the 56dB or something to do with that unexplained 400000?

If I use the 56dB as the SNR then I get C = 23331bps. I've got no reference to know if that's correct.

Check this out:
http://en.wikipedia.org/wiki/Decibel

400000 = 10^(56/10)

log base 2 or infact log base anything is quite the same as log base 10

here is a simple explanation

Supose you have 8=2^x where u need to find x, the question is at what power should 2 be raised to get 8

to solve this question, u need t use logs.....where x=log base 2 of 8 or ((log_2)8)

infact: a=b^x can be solved for x using x= log base b of a ((log_b)a)

in a standard calculator, log is always on base 10so if u have 100=10^x, x=log_10 of 100, so if u calculate using a calculator, you would type log_10 of 100 which would give you 2, since 10 raised to the power of 2 gives 100

coming to where the base is not 10 and that u cant use a calculator, u need to change the base,

a simple base change can be done where log base a of b ((log_a)b) equals to the log base 10 of b devided by the log base 10 of a (log b)/(log a) note that when not specified, the base is always 10

hence, if u were to solve x for 8=2^x

x=log base 2 of 8 which is also equal to log base 10 of 8 devided by log base 10 of 2 or (Log 8)÷(Log 2).... try it in your calculator that is gives 3 since 2 raised to the power 3 gives 8........hope that helped u

I have the same exact problem in my text book... Is it "wireless communications & networks" by William Stallings?

The (400000) is the 56dB that they took out of 56dB for you... heres the mathematical relationship they didnt include : 10 log(400000) = 56 dB

400000 is the SNR that has to be taken out of dB so it can be used in the following formula which is Shannon's Theorm

C = B log_2(1+ SNR)

where,

SNR = signal-to noise ratio
C= channel capacity
B= Bandwidth ( I believe)

So, I'm guessing that to use this formula we gotta figure out what the bandwidth of telephone is.

Hope this helps...

It is Log base 2. To calculate with standard log base 10 all you need to do is:

Log (x)
---------
Log 2