2.647*0.427/0.05738

Question

Use log table to evaluate

Answer 1

To evaluate the expression $\frac{2.647\times 0.427}{0.05738}$ using logarithms, we can follow these steps:

1. Convert the numbers to logarithmic form:

   Let's denote: $$A=2.647,B=0.427,C=0.05738$$

   We need to calculate $\log (A\times B)$ and then subtract $\log (C)$.

2. Find the logarithms of each number using a logarithm table (base 10):

   • For $A=2.647$: $$\log (2.647)\approx 0.423$$
   • For $B=0.427$: $$\log (0.427)=\log (4.27)-1\approx 0.630-1=-0.370$$
   • For $C=0.05738$: $$\log (0.05738)=\log (5.738)-2\approx 0.759-2=-1.241$$

3. Calculate the logarithm of the product: $$\log (A\times B)=\log (2.647)+\log (0.427)=0.423-0.370=0.053$$

4. Calculate the logarithm of the division: $$\log \left(\frac{A\times B}{C}\right)=\log (A\times B)-\log (C)=0.053-(-1.241)=0.053+1.241=1.294$$

5. Convert back from log to find the final result: The result can be obtained by taking the antilogarithm: $$\text{Result}={10}^{1.294}\approx 19.67$$

Therefore, the final evaluation of $\frac{2.647\times 0.427}{0.05738}$ is approximately 19.67.