To evaluate the expression \( \frac{2.647 \times 0.427}{0.05738} \) using logarithms, we can follow these steps:
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Convert the numbers to logarithmic form:
Let's denote: \[ A = 2.647, \quad B = 0.427, \quad C = 0.05738 \]
We need to calculate \( \log(A \times B) \) and then subtract \( \log(C) \).
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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 \( C = 0.05738 \): \[ \log(0.05738) = \log(5.738) - 2 \approx 0.759 - 2 = -1.241 \]
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Calculate the logarithm of the product: \[ \log(A \times B) = \log(2.647) + \log(0.427) = 0.423 - 0.370 = 0.053 \]
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Calculate the logarithm of the division: \[ \log\left(\frac{A \times B}{C}\right) = \log(A \times B) - \log(C) = 0.053 - (-1.241) = 0.053 + 1.241 = 1.294 \]
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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.
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