Question

Evaluate with the use of logarithm table 0.3581 multiply by 0.02847 / 0.009418 multiply 3.219

Answer 1

To evaluate the expression \( \frac{0.3581 \times 0.02847}{0.009418 \times 3.219} \) using logarithms, we proceed as follows:

1. **Take logarithm on both sides**: We'll use logarithmic properties to transform our expression.

\[
\log_{10}(A) = \log_{10}(0.3581) + \log_{10}(0.02847) - \log_{10}(0.009418) - \log_{10}(3.219)
\]

2. **Find logarithm values**: Using a logarithm table, we find:
- \( \log_{10}(0.3581) \approx -0.446 \)
- \( \log_{10}(0.02847) \approx -1.570 \)
- \( \log_{10}(0.009418) \approx -2.026 \)
- \( \log_{10}(3.219) \approx 0.男232 \)

3. **Calculate the combined logarithm**:
\[
\log_{10}(A) = -0.446 - 1.570 + 2.026 - 0.232
\]

- Combining these values:
\[
-0.446 - 1.570 = -2.016
\]
\[
-2.016 + 2.026 = 0.01
\]
\[
0.01 - 0.232 = -0.222
\]

4. **Convert back from logarithm**: Now we find \( A \):
\[
A = 10^{-0.222}
\]

To evaluate \( 10^{-0.222} \), you can use a calculator:
\[
A \approx 0.601
\]

So the final answer is:

\[
\frac{0.3581 \times 0.02847}{0.009418 \times 3.219} \approx 0.601
\]