2. How many binary digits are there in the numbers 2100, 5100 and 10100? How are the answers to these three questions related? (Hint: this is a question about logarithms and change of base.) * 3. (a) Show that log(x) = c log(x) for some constant c (expressed only in terms of the constants a and b). Hint: This is probably easier than you think... It follows quite directly from the log properties. You should, though, prove that it's true for any a and b and not prove by an example. (b) Calculate the ratio between the number of digits required to write a number in base 10 and the number of digits required to write the same number in base 2. Notice that this question relates to question 2 and 3a above.