To calculate \(2.267 \times 0.0921\) using logarithms, follow these steps:
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Find the logarithms of each number.
Using logarithm tables or a calculator:
- \(\log_{10}(2.267) \approx 0.3565\)
- \(\log_{10}(0.0921) \approx -1.0345\)
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Add the logarithms.
\[ \log_{10}(2.267 \times 0.0921) = \log_{10}(2.267) + \log_{10}(0.0921) \]
\[ = 0.3565 - 1.0345 = -0.678 \]
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Convert the logarithm back to standard form.
To find the result: \[ 2.267 \times 0.0921 = 10^{-0.678} \] You can calculate \(10^{-0.678}\) using a calculator: \[ 10^{-0.678} \approx 0.208 \]
Tabular Form
Here's how you can represent this in a tabular form:
| Step | Value | |------------------------------------|--------------| | Value 1 | 2.267 | | Logarithm of Value 1 | \( \log_{10}(2.267) \approx 0.3565 \) | | Value 2 | 0.0921 | | Logarithm of Value 2 | \( \log_{10}(0.0921) \approx -1.0345 \) | | Sum of Logarithms | \( -0.678 \) | | Result \( (2.267 \times 0.0921) \)| \( 10^{-0.678} \approx 0.208 \) |
So, the multiplication of \(2.267\) and \(0.0921\) is approximately \(0.208\).