log_a(25) = log_a(5^2) = 2 log_a(5) = 2p, hence q = 2p.

log_a(25) = log_a(5^2) = 2 log_a(5) = 2p, hence q = 2p.

log_a(64) = 6 implies a^6 = 64. Since 64 = 2^6, we have a = 2.

From the definition of logarithms, b = a^c.

The expression log_a(b) = c can be rewritten in exponential form as a^c = b.

The definition of logarithms states that if log_a(b) = c, then a raised to the power of c equals b, hence a^c = b.

log_a(bc) = log_a(b) + log_a(c) = p + q.

log_a(bc) = log_a(b) + log_a(c) = p + q.

By the definition of logarithms, if log_a(b) = x, then b = a^x.

log_b(25) = 2 implies b^2 = 25. Therefore, b = 5.

log_b(27) = 3 implies b^3 = 27 => b = 3.

The definition of logarithms states that if log_b(x) = y, then b raised to the power of y equals x, hence b^y = x.

log_x(16) = 4 implies x^4 = 16 => x^4 = 2^4 => x = 2.

log_x(27) = 3 implies x^3 = 27 => x = 3.

log_x(4) = 2 implies x^2 = 4 => x = 2.

log_x(64) = 6 implies x^6 = 64. Since 64 = 2^6, we have x = 2.

log_x(81) = 4 implies x^4 = 81 => x^4 = 3^4 => x = 3.

log_x(81) = 4 implies x^4 = 81 => x = 3.

M · N = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

M · N = 2*3 + 2*3 + 2*3 = 6 + 6 + 6 = 18.

M is between N and O, so O is next to M, making M the answer.

With M opposite N and O to the right of M, P must be to the left of N, completing the arrangement.

The arrangement can be visualized as M-N-P-O-Q-R-S. Therefore, P is sitting opposite N.

With M to the right of N, we can visualize the arrangement. O's position opposite M helps us determine that Q is to the left of N.

M is the father of O, making M the father of N's father.

M is the aunt of O because she is the sister of O's father, N.

M is the uncle of N, which means M is the brother of N's parent O, making M the brother-in-law of O.

From M ≥ N and N > O, we can conclude M > O.

15 days from Monday is Wednesday.

Since O is next to N, P, Q, and R are not specified to be next to O.