Inverse proportion. M1 * D1 = M2 * D2. 45 * 16 = x * 24. Solving for x gives x = (45 * 16) / 24 = 720 / 24 = 30 men.

Using (M1 * D1) / W1 = (M2 * D2) / W2. We have (7 * 7) / 7 = (1 * x) / 1. Simplifying, we get 7 = x. So, it takes 7 days.

Using the chain rule formula: (M1 * D1) / W1 = (M2 * D2) / W2. Here, (20 * 6) / 112 = (25 * 3) / x. This simplifies to 120 / 112 = 75 / x. Thus, x = (112 * 75) / 120 = 70 meters.

This is an inverse proportion. M1 * D1 = M2 * D2. We have 15 * 28 = 10 * x. Thus, x = (15 * 28) / 10 = 420 / 10 = 42 days.

This is a direct proportion. More length means more weight. 12 / 42 = 20 / x. So, x = (42 * 20) / 12 = 70 kg.

This is an inverse proportion. Less men will take more days. Formula: M1 * D1 = M2 * D2. So, 36 * 18 = 27 * x. Solving for x gives x = (36 * 18) / 27 = 24 days.

This is a direct proportion. Let the required cost be x. 15 / 234 = 35 / x. Cross-multiplying gives 15x = 234 * 35. Therefore, x = (234 * 35) / 15 = 546.

Express both numbers with the base 2. 8 = 2^3 and 16 = 2^4. Substitute these into the equation: (2^3)^x = 2^4, which is 2^(3x) = 2^4. Equating the exponents gives 3x = 4. Dividing by 3 gives x = 4/3.

Rewrite 36 as 6^2. The equation becomes (6^2)^x = 6^1, or 6^(2x) = 6^1. Equating the exponents gives 2x = 1. Solving for x yields x = 0.5 (which is the same as the square root).

Any non-zero base raised to the power of 0 equals 1. Thus, we can rewrite 1 as 7^0. The equation is 7^(2x-1) = 7^0. Equating exponents: 2x - 1 = 0, which gives 2x = 1, and x = 0.5.