To evaluate the expression \( \frac{0.3581 \times 0.02847}{0.009418 \times 3.219} \) using logarithms, we proceed as follows:
-
Take logarithm on both sides: We'll use logarithmic properties to transform our expression.
\[ \log_{10}(A) = \log_{10}(0.3581) + \log_{10}(0.02847) - \log_{10}(0.009418) - \log_{10}(3.219) \]
-
Find logarithm values: Using a logarithm table, we find:
- \( \log_{10}(0.3581) \approx -0.446 \)
- \( \log_{10}(0.02847) \approx -1.570 \)
- \( \log_{10}(0.009418) \approx -2.026 \)
- \( \log_{10}(3.219) \approx 0.男232 \)
-
Calculate the combined logarithm: \[ \log_{10}(A) = -0.446 - 1.570 + 2.026 - 0.232 \]
- Combining these values: \[ -0.446 - 1.570 = -2.016 \] \[ -2.016 + 2.026 = 0.01 \] \[ 0.01 - 0.232 = -0.222 \]
-
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:
\[ \frac{0.3581 \times 0.02847}{0.009418 \times 3.219} \approx 0.601 \]