Use logarithms to evaluate (58.72 x 406)/(0.845). A farmer fenced a rectangular plot of land. The length of the plot is 3 metres more than its width. Given that the total area of the plot is 180 m2. F

Here are the solutions to the questions from the image:

16. Use logarithms to evaluate $\frac{58.72 \times 406}{0.845}$.

Step 1: Let $N = \frac{58.72 \times 406}{0.845}$.

Step 2: Take the logarithm of both sides.

$$\log N = \log(58.72) + \log(406) - \log(0.845)$$

Step 3: Find the logarithms of each number using a logarithm table.

• $\log(58.72) = 1.7690$
• $\log(406) = 2.6085$
• $\log(0.845) = \bar{1}.9269$

Step 4: Perform the addition for the numerator.

$$\log(58.72 \times 406) = 1.7690 + 2.6085 = 4.3775$$

Step 5: Perform the subtraction.

$$\log N = 4.3775 - \bar{1}.9269$$ $$\log N = 4.3775 - (-1 + 0.9269)$$ $$\log N = 4.3775 + 1 - 0.9269$$ $$\log N = 5.3775 - 0.9269$$ $$\log N = 4.4506$$

Step 6: Find the antilogarithm of 4.4506.

$$\text{Antilog}(0.4506) \approx 2.822$$ $$N = 2.822 \times 10^4$$ $$N = \boxed{28220}$$

17. A farmer fenced a rectangular plot of land. The length of the plot is 3 metres more than its width. Given that the total area of the plot is 180 m$^2$.