Evaluate using logarithm table 7.143×821.5÷0.0014
To evaluate 7.143×821.5÷0.0014 using logarithm table, we can take the logarithm of each number involved and then perform the necessary calculations.
Let's begin by taking the logarithm of each number:
log(7.143) = 0.854
log(821.5) = 2.914
log(0.0014) = -2.853
Next, we can rewrite the expression in terms of logarithms:
log(7.143×821.5÷0.0014) = log(7.143) + log(821.5) - log(0.0014)
Substituting the logarithm values, we get:
log(7.143×821.5÷0.0014) = 0.854 + 2.914 - (-2.853)
Simplifying, we have:
log(7.143×821.5÷0.0014) = 0.854 + 2.914 + 2.853
log(7.143×821.5÷0.0014) = 6.621
Finally, we can find the antilogarithm of 6.621 to obtain the answer:
antilog(6.621) = 7688.366
Therefore, 7.143×821.5÷0.0014 is approximately equal to 7688.366.
To evaluate the expression 7.143 × 821.5 ÷ 0.0014 using logarithm tables, we can use the property of logarithms that states: log(a × b) = log(a) + log(b) and log(a ÷ b) = log(a) - log(b).
Given expression: 7.143 × 821.5 ÷ 0.0014
Using logarithm tables, we can rewrite the expression as:
log(7.143) + log(821.5) - log(0.0014)
Now, let's look up the logarithms of each term using the logarithm table.
1. log(7.143):
From the logarithm table, log(7.1) = 0.8513 and log(7.2) = 0.8561.
Since 7.143 lies between these two values, we can estimate that log(7.143) ≈ 0.8537.
2. log(821.5):
We can see from the logarithm table that log(821) = 2.9149 and log(822) = 2.9156.
Again, estimating the value for 821.5, we get log(821.5) ≈ 2.9153.
3. log(0.0014):
As we need to find log(0.0014), we can rewrite it as log(1.4 × 10^(-3)).
From the logarithm table, log(1.4) = 0.1461 and log(10^(-3)) = -3.
Adding these two values, we get log(1.4 × 10^(-3)) ≈ -2.8539.
Now, substitute the estimated logarithms back into the expression:
0.8537 + 2.9153 - (-2.8539)
Simplifying further:
0.8537 + 2.9153 + 2.8539
Finally, perform the addition:
6.6229
Therefore, evaluating the expression using logarithm tables, we get:
7.143 × 821.5 ÷ 0.0014 ≈ 6.6229.