log2(8) = log2(2^3) = 3.

27 = 3^3, so x = 3.

log3(9) = 2 and log3(3) = 1, so x = 2 + 1 = 3.

x = 16^(1/4) = 2.

O is the father of N, making him the son of M.

n - 1 is odd since subtracting 1 from an even number results in an odd number.

Both n + 1 and n - 1 are even, and 2n is always even.

The arrangement is Q, P, R. P is between Q and R.

R is the brother of Q, and since P is the sister of Q, R is also P's brother.

Let Q2 sales be x. Then Q1 sales = 0.5x. If Q2 sales = 200, then Q1 sales = 0.5 * 200 = 100.

The arrangement is V, S, T, U. U is to the right of T.

U is the son of T, and since S is the daughter of T, U is S's brother.

The arrangement is U, V, T. V is in the middle.

Sum = Average × Number of items = 20 × 10 = 200.

Average = Sum of numbers / Number of numbers. Therefore, Sum = Average * Number = 20 * 5 = 100.

D=4, O=15, G=7; C=3, A=1, T=20. The code for 'CAT' is 3120.

Let Principal = P. Then, CI = P(1 + r/100)^n - P = P(1 + 0.1)^2 - P = P(1.21 - 1) = 0.21P. Given CI = 121, we have 0.21P = 121, thus P = 121 / 0.21 = $1000.

Using the formula for compound interest, A = P(1 + r/n)^(nt). Here, A = P + 121, r = 0.1, n = 1, t = 2. Solving gives P = 1000.

If the day before yesterday was Friday, then today is Sunday.

If today is Sunday, then two days after tomorrow (Tuesday) is Sunday.

Circumference = πd = π(10) ≈ 31.4 m.

If the HCF is 1, the numbers are coprime, meaning they have no common factors other than 1.

The product of the two numbers is equal to the product of their HCF and LCM, which is 15 * 150 = 2250.

If the HCF is equal to one of the numbers, it means that one number is a multiple of the other.

The other number can be found using the formula: LCM = (a * b) / HCF. Here, 120 = (30 * b) / HCF. Assuming HCF is 30, b = 120 / 30 = 40.

The product of the two numbers is LCM * HCF = 36 * 6 = 216.

The product of the two numbers is HCF * LCM = 5 * 60 = 300.

The other number can be found using the formula LCM(a, b) = (a * b) / HCF(a, b). Here, 72 = (8 * x) / HCF(8, x). The other number is 18.

The other number can be found using the formula: LCM = (a * b) / HCF. Here, 84 = (12 * b) / HCF. The other number is 28.

Area = length × width; if length is doubled, area also doubles.