According to the ShannonHartley theorem the capacity of a co

According to the Shannon-Hartley theorem, the capacity of a communications channel in bits per second is given by C=Blog₂ ((s/n)+1) where B is the frequency bandwidth of the channel in hertz and s/n is its signal-to-noise ratio. It is physically impossible to exceed this limit. Solve the equation for the signal-to-noise ratio s/n.

Solution

C = B*log2( 1+s/n)

divide both sides by B:

(C/B) = log2(1+s/n)

Use the log property : loga(b) = x ----: b = a^x

So, 1+ s/n = 2^(C/B)

( signal-to-noise ratio) S/N = 2^(C/B) -1