Question:

1. If P represents the product of all prime numbers less than 1000, what is the value of the unit's digit of P?

2. Do any real numbers a and b exist such that: ln(a+b)=ln a + ln b? if so, what are they?

3. Define a function by: f(x)=1/1-x where x is not equal to 0,1. what is f(f(f(a)))?

1. Two of the primes less than 1000 are 2 and 5.
2. Since ln a + ln b = ln(ab) this question is equivalent to asking:
   Do any positive real numbers a and b exist such that: a+b = ab?
3. Since f(x) = 1/(1-x) it follows that f(f(a)) = 1/(1-f(a)). Substitute f(a) = 1/(1-a) and simplify. Now find f(f(f(a))) = 1/(1-f(f(a))).

Cheers,
Harley