(1) Prove: log2 5 is irrational.
Suppose log2 5 = a / b where a and b are integers. By the property of logs, 2a/b = 5., which implies that 2a = 5b. Thus, 2a = 5b is an integer that is both even and odd. This is a contradiction which implies that log2 5 cannot be represented by the fraction a / b and is therefore irrational.