Sarah is the mother of Mary, making her the grandmother of John.

Susan is John's grandmother because she is the mother of Mary, who is John's mother.

Tom is the uncle of John because he is the brother of John's mother, Mary.

If 'a' is excluded, we can form subsets from {b, c}, which has 2^2 = 4 subsets.

K is to the right of L and M is to the left of K, making K the middle person.

Since L is between M and N, and O is opposite L, N must be to the right of O.

The arrangement is O, L, M, N. N is sitting to the right of M.

Since L is to the right of M, and N is opposite L, M must be to the left of N.

If L is to the right of M, then O must be to the left of M, as N is opposite L.

Since L is not next to M, it is possible for P to be next to L, making this statement true in some arrangements.

N is between O and P, so N is next to P. L and M being opposite does not affect this arrangement.

Using the grating equation d sin(θ) = mλ, where d = 1/1000 mm = 1 x 10^-6 m, for m=1, we find θ ≈ 30 degrees.

Anna is Lisa's sister.

log(2x) = 3 => 2x = 10^3 => x = 1000.

log_10(0.01) = log_10(10^-2) = -2, so x = -2.

Since 1000 = 10^3, log_10(1000) = 3, thus x = 3.

log_10(10^x) = x. Therefore, x = 2.

log_10(20) = log_10(2) + log_10(10) = 0.301 + 1 = 1.301.

log_10(20) = log_10(2 * 10) = log_10(2) + log_10(10) = a + 1.

log_10(x) = 2 implies x = 10^2 = 100.

log_2(8) = 3 and log_2(4) = 2, thus x = 3 + 2 = 5.

Since 8 is 2^3, log_2(8) equals 3.

log_2((x + 1)/x) = 1 implies (x + 1)/x = 2 => x + 1 = 2x => x = 1.

log_2(x + 1) = 3 implies x + 1 = 2^3 = 8 => x = 7.

log_2(x) + 2 = 5 => log_2(x) = 3 => x = 2^3 = 8.

log_2(x) + 2 = 5 implies log_2(x) = 3, thus x = 2^3 = 8.

log_2(x) + 2 = 6 implies log_2(x) = 4, so x = 2^4 = 16.

log_2(x(x - 3)) = 3 => x(x - 3) = 2^3 = 8 => x^2 - 3x - 8 = 0. Solving gives x = 6.

log_2(x(x-1)) = 3 => x(x-1) = 2^3 = 8 => x^2 - x - 8 = 0. Solving gives x = 5.

log_2(x) = 5 implies x = 2^5 = 32.