Question
With the use of logarithm table calculate 5.25x23.73
Answers
GPT-4o mini
To calculate \( 5.25 \times 23.73 \) using logarithm tables, you can follow these steps:
1. **Find the logarithms** of the numbers:
- Look up the logarithm of \( 5.25 \).
- Look up the logarithm of \( 23.73 \).
2. **Add the logarithms**:
\[
\log(5.25) + \log(23.73) = \log(5.25 \times 23.73)
\]
3. **Find the antilogarithm** (or exponentiate) of the result to get the product.
Let's assume you have access to logarithm tables (for base 10), where you find:
- \( \log(5.25) \approx 0.720 \) (the exact value may vary slightly based on the table)
- \( \log(23.73) \approx 1.376 \) (again, this is an approximate value)
Now, perform the addition:
\[
\log(5.25) + \log(23.73) \approx 0.720 + 1.376 = 2.096
\]
Finally, find the antilogarithm:
- From the table, you would find the value corresponding to \( 2.096 \).
- The antilogarithm of \( 2.096 \approx 124.5 \) (you may get a slightly different value based on the precision of the logarithm table you are using).
Thus, the product \( 5.25 \times 23.73 \approx 124.5 \).
For the most precise results, ensure you use the tables you have available to retrieve the logarithm values directly and perform an accurate addition and conversion.
1. **Find the logarithms** of the numbers:
- Look up the logarithm of \( 5.25 \).
- Look up the logarithm of \( 23.73 \).
2. **Add the logarithms**:
\[
\log(5.25) + \log(23.73) = \log(5.25 \times 23.73)
\]
3. **Find the antilogarithm** (or exponentiate) of the result to get the product.
Let's assume you have access to logarithm tables (for base 10), where you find:
- \( \log(5.25) \approx 0.720 \) (the exact value may vary slightly based on the table)
- \( \log(23.73) \approx 1.376 \) (again, this is an approximate value)
Now, perform the addition:
\[
\log(5.25) + \log(23.73) \approx 0.720 + 1.376 = 2.096
\]
Finally, find the antilogarithm:
- From the table, you would find the value corresponding to \( 2.096 \).
- The antilogarithm of \( 2.096 \approx 124.5 \) (you may get a slightly different value based on the precision of the logarithm table you are using).
Thus, the product \( 5.25 \times 23.73 \approx 124.5 \).
For the most precise results, ensure you use the tables you have available to retrieve the logarithm values directly and perform an accurate addition and conversion.