Evaluate with the help of Logarithms 1) 2391/3072 2.38*3.901/4.83
let x = 2391/3072 2.38*3.901/4.83
log x = log (2391/3072 2.38*3.901/4.83)
= log(2391) - log(3072) + log(2.38) + log(3.901) - log(4.83)
= 0.17496
x = 1.496
my calculator answer: 1.496 to 3 decimals
This is the kind of question I actually taught about 45 years ago.
In those days we had Log-tables that were only correct to about 3 decimals.
To do the question the way I typed it, I actually used my calculator to get the log values.
Today, such a question would only have significance from a historical viewpoint.
Are you still given log tables?
If not, how does your teacher expect you to do this without tables?
This type of question is similar to asking a carpenter today to build a piece of furniture without any power tools.
Well, if you want me to evaluate something using logarithms, I guess I could try to be helpful while throwing in a joke or two!
1) To evaluate 2391/3072, you can use logarithms if you want, but it might be a bit of an overkill. Instead, why not just use a calculator? They're logarithmically (logarithmically, get it?) better at crunching numbers! The answer is approximately 0.7788.
2) Now we have 2.38 * 3.901 / 4.83. You could use logarithms to evaluate this, but unless you're having a logarithmic party, it's not really necessary. So, my advice is to grab your trusty calculator again! The answer to this one is approximately 1.9149.
Remember, logarithms can be useful in certain cases, but for simple divisions and multiplications, a good old calculator will do the trick without any logarithmic headaches!
1) To evaluate 2391/3072 using logarithms, we can use the property of logarithms which states that log(a/b) = log(a) - log(b).
Step 1: Take the logarithm of the numerator (2391).
log(2391) ≈ 3.3793
Step 2: Take the logarithm of the denominator (3072).
log(3072) ≈ 3.4871
Step 3: Subtract the logarithm of the denominator from the logarithm of the numerator.
log(2391/3072) = log(2391) - log(3072) ≈ 3.3793 - 3.4871 ≈ -0.1078
Therefore, 2391/3072 ≈ 10^(-0.1078) ≈ 0.8882.
2) Evaluating 2.38*3.901/4.83 using logarithms:
Step 1: Take the logarithm of each number using a calculator.
log(2.38) ≈ 0.3765
log(3.901) ≈ 0.5893
log(4.83) ≈ 0.6831
Step 2: Add the logarithms of 2.38 and 3.901.
0.3765 + 0.5893 ≈ 0.9658
Step 3: Subtract the logarithm of 4.83 from the sum obtained in step 2.
0.9658 - 0.6831 ≈ 0.2827
Step 4: Raise 10 to the power of the result obtained in step 3.
10^(0.2827) ≈ 1.7954
Therefore, 2.38*3.901/4.83 ≈ 1.7954.
To evaluate these expressions using logarithms, we can utilize the properties of logarithms and convert the division and multiplication operations into addition and subtraction operations.
1) Evaluating 2391/3072 using logarithms:
First, let's take the logarithm (base 10) of both the numerator and denominator to convert the division into subtraction:
log(2391/3072) = log(2391) - log(3072)
Next, we can use a scientific calculator or logarithmic table to find the logarithm of each number:
log(2391) ≈ 3.378
log(3072) ≈ 3.487
Substituting the values back into the equation:
log(2391/3072) ≈ 3.378 - 3.487 = -0.109
Therefore, 2391/3072 ≈ 10^(-0.109) ≈ 0.8772 (approximately)
2) Evaluating 2.38*3.901/4.83 using logarithms:
First, let's calculate the logarithm (base 10) of each number:
log(2.38) ≈ 0.377
log(3.901) ≈ 0.590
log(4.83) ≈ 0.683
Now, let's convert the multiplication and division into addition and subtraction:
2.38*3.901/4.83 can be rewritten as 10^(log(2.38) + log(3.901) - log(4.83))
Substituting the values into the equation:
10^(0.377 + 0.590 - 0.683) ≈ 10^0.284 ≈ 1.774 (approximately)
Therefore, 2.38*3.901/4.83 ≈ 1.774 (approximately)