I had a question about the properties of logarithms and exponents, that I need some assistance on:
If you are familiar with electrical engineering principles, you may be familiar with Shannon's Channel Capacity Theorem:
$$C = W\log_2(1 + \text{SNR})$$
Where $W$ represents the bandwidth and $C$ is the capacity of the channel. Well it can be found such that
$$\text{SNR} = \dfrac{E_b}{N_0}\cdot \dfrac{C}{W}$$
If we take the above, and replace it into the original capacity equation, we get:
$$C = W \log_2\biggl(1 + \dfrac{E_b}{N_0}\cdot \dfrac{C}{W}\biggr) = W \cdot 2^{\bigl(1 +\frac{E_b}{N_0} \cdot \frac{C}{W}\bigr)}$$
However, this is where I'm kinda stuck. I would like to solve for $E_b/N_0$, but I'm a bit rusty on my algebra. This might be a rather simple question, but are there some properties of exponents or logs that I can leverage to solve for $E_b/N_0$?
Thanks for your help in advanced! I really appreciate it!