Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)

Which is the biggest and which the smallest of these numbers?

$$2000^{2002} \quad\quad 2001^{2001}\quad\quad 2002^{2000} $$

How do they compare in magnitude?