Evaluate, using logarithm table 0.0935×8.672?
so, go to your log table.
Remember that
log(0.0935×8.672) = log 0.0935 + log 8.672 = -1.029188 + 0.938119 = -0.0910687
Now take the antilog
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To evaluate the expression 0.0935 × 8.672 using a logarithm table, we can take the logarithm of both numbers, add them, and then find the antilogarithm of the result.
1. Find the logarithm of 0.0935:
- Look up the logarithm in the table for 0.0935. Let's say it is -1.97 (approximately).
2. Find the logarithm of 8.672:
- Look up the logarithm in the table for 8.672. Let's say it is 0.9392 (approximately).
3. Add the logarithms:
- Summing -1.97 and 0.9392 gives -1.0308 (approximately).
4. Find the antilogarithm of -1.0308:
- Use the antilogarithm table or calculator to find the value corresponding to -1.0308. Let's say it is 0.0968 (approximately).
Therefore, when evaluated using a logarithm table, 0.0935 × 8.672 is approximately equal to 0.0968.
To evaluate the expression 0.0935 × 8.672 using a logarithm table, we can utilize the properties of logarithms and exponentiation. Here's the step-by-step process:
Step 1: Take the logarithm of each number.
Looking at the expression 0.0935 × 8.672, we can take the logarithm of both values separately. We'll use base 10 logarithms (common logarithms), denoted as log10.
log10(0.0935) ≈ -1.0294
log10(8.672) ≈ 0.9393
Step 2: Add the logarithms.
Now, we add the logarithms of the two numbers we obtained in Step 1.
-1.0294 + 0.9393 ≈ -0.0901
Step 3: Find the antilogarithm.
To find the value corresponding to the sum of logarithms, we need to take the antilogarithm (also called exponentiation) using base 10.
Using the logarithm table, we can look for the value closest to -0.0901. In the table, we find that log10(0.562) ≈ -0.2501, and log10(0.561) ≈ -0.2519.
Since -0.0901 falls between -0.2501 and -0.2519, we can interpolate to find the corresponding value.
0.562 ≈ 0.561 * (√((-0.0901 + 0.2519) / (-0.2501 + 0.2519))))
≈ 0.561 * √(0.648)
≈ 0.561 * 0.804
≈ 0.451
Therefore, the evaluation of 0.0935 × 8.672 using a logarithm table is approximately 0.451.