Evaluate the square root of 82.41*76.52 divided by 7.839 using logarithm tables

Answer 1

To evaluate this expression using logarithm tables, we will make use of the property of logarithms that allows us to convert division into subtraction.

First, let's find the logarithm of the expression 82.41*76.52 divided by 7.839.

Log(82.41*76.52/7.839)

Using logarithm rules, we can simplify this expression by taking the logarithm of each term separately and then subtracting the logarithm of the denominator:

Log(82.41) + Log(76.52) - Log(7.839)

Now, let's look up the logarithms of each term in the table:

Log(82.41) = 1.9158
Log(76.52) = 1.8830
Log(7.839) = 0.8938

Finally, substitute these values back into the expression:

1.9158 + 1.8830 - 0.8938 ≈ 2.905

So, the approximate value of the square root of (82.41*76.52)/7.839, using logarithm tables, is 2.905.

Answer 2

wrong again
as you say, Log(82.41*76.52/7.839)
= Log(82.41) + Log(76.52) - Log(7.839) = 2.905
That means Log√(82.41*76.52/7.839) = 1.453
so √(82.41*76.52/7.839) = 10^1.453 = 28.379

Answer 3

Apologies for the mistake. You are correct. Using logarithm tables, we can evaluate the square root of (82.41*76.52)/7.839 as follows:

Log(82.41*76.52/7.839) = Log(82.41) + Log(76.52) - Log(7.839)

From the logarithm table:

Log(82.41) = 1.9158
Log(76.52) = 1.8830
Log(7.839) = 0.8938

Substituting these values back into the expression:

Log(82.41) + Log(76.52) - Log(7.839) = 1.9158 + 1.8830 - 0.8938 ≈ 2.905

As you mentioned, Log√(82.41*76.52/7.839) = 1.453

Using the property that exponentiating both sides with base 10 gives us:

10^(Log√(82.41*76.52/7.839)) = 10^(1.453)

Therefore, the square root of (82.41*76.52)/7.839 is approximately:

√(82.41*76.52/7.839) ≈ 10^1.453 ≈ 28.379

Thank you for pointing out the error, and I apologize for any confusion caused.