Finding the capacity of a Signal

Question

I've labelled the image with my questions. Using the Claude Shannon expression we have to find the capacity of this signal.

Answer 1

The logarithm of a number is the exponent to which we have to raise the base to get that number. In this case we have:

$$\log_{10}(S/N)=3$$

so the base is $10$, the number is $S/N$ and the exponent (Thebes's value of the logarithm) is $3$, hence by definition of logarithm we get:

$$10^3=S/N.$$

For the second issue, we want to evaluate $\log_2(1001)$, but we prefer to change the base; this is possible by means the following formula:

$$\log_ab={\log_cb\over\log_ca}$$

so $\log_21001={\log_{10}1001\over\log_{10}2}$, now you can calculate it by your calculator.