The area of a rectangular farm is 7462m². The width of the farm is 82m. Use logarithm tables to determine the length of the farm.

Step 1: State the formula for the area of a rectangle and rearrange it to find the length. The area of a rectangle ($A$) is given by the formula $A = length \times \text{width}$. Given $A = 7462 m^2$ and width $w = 82 \text{ m}$. We need to find the length $l$. $l = \frac{A}{w} = \frac{7462}{82}$

Step 2: Express the division using logarithms. To use logarithm tables, we convert the division into a subtraction of logarithms. $\log l = \log\left(\frac{7462}{82}\right) = \log(7462) - \log(82)$

Step 3: Find $\log(7462)$ using logarithm tables. The characteristic of $\log(7462)$ is 3 (since $7462 = 7.462 \times 10^3$). From logarithm tables, the mantissa for 746 is 0.8727. The mean difference for 2 is 1. So, the mantissa for 7462 is $0.8727 + 0.0001 = 0.8728$. $\log(7462) = 3.8728$

Step 4: Find $\log(82)$ using logarithm tables. The characteristic of $\log(82)$ is 1 (since $82 = 8.2 \times 10^1$). From logarithm tables, the mantissa for 820 is 0.9138. $\log(82) = 1.9138$

Step 5: Subtract the logarithms. $\log l = 3.8728 - 1.9138$ $\log l = 1.9590$

Step 6: Find the antilogarithm of $1.9590$ to determine the length. The characteristic is 1, which means the number has two digits before the decimal point. From antilogarithm tables, the antilog of $0.9590$ is approximately $9.099$. Multiplying by $10^1$ (due to the characteristic of 1): $l = 9.099 \times 10^1 = 90.99$ The length of the farm is approximately $90.99$ m.

$\boxed{90.99 m}$