To solve the expression \( \frac{1.487^3 - 1}{1.487^3 + 1} \) for \( 1.487 \) using logarithms and antilogs, we can follow these steps:
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Calculate \( 1.487^3 \) using logarithms:
- Use the property: \( \log(a^b) = b \cdot \log(a) \).
First, we find \( \log(1.487) \):
- For example, from a logarithm table (or calculator), we find: \[ \log(1.487) \approx 0.1710 \text{ (you may need a specific log table )} \]
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Calculate \( \log(1.487^3) \): \[ \log(1.487^3) = 3 \cdot \log(1.487) \approx 3 \cdot 0.1710 \approx 0.5130 \]
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Find the antilog of \( 0.5130 \): \[ 1.487^3 \approx 10^{0.5130} = 3.247 \] (check the log table for \( 10^{0.5130} \) or use a calculator)
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Calculate the entire expression: \[ \text{Substituting the value, we have: } 1.487^3 - 1 \approx 3.247 - 1 = 2.247 \] \[ 1.487^3 + 1 \approx 3.247 + 1 = 4.247 \]
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Now calculate the final expression: \[ \frac{1.487^3 - 1}{1.487^3 + 1} = \frac{2.247}{4.247} \]
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Using a calculator to get the decimal: \[ \frac{2.247}{4.247} \approx 0.529 \]
Thus, \( \frac{1.487^3 - 1}{1.487^3 + 1} \approx 0.529 \).