Evaluate the Following Using logarithm
Table
1) 5.25 Multiplied by 23.73
I doubt if many people will read this, but it was fun doing it...
My goodness, I recall teaching this over 50 years ago.
You mean to tell me, this is still on your curriculum???
Dilemma :
If your text still has tables in the back of the book, it must be over
25 years old, and it is time to get a new text from your school board.
If you don't have tables, then you must use a calculator.
If your calculator can do logs, then surely it can do basic multiplication.
after about 1990, I would use this type of question only as a "historical
novelty" in the introduction to logarithms.
Here are the actual steps needed to do it the old way:
let x = 5.25*23.73
log x = log 5.25 + log 23.73
log 5.25 = .7202 , most tables only had 4 digits
log 23.73
= log (2.373 * 10^1)
= .3753 + 1 = 1.3753
log x = log 5.25 + log 23.73
= .7202 + 1.3753
= 2.0955
then x = 10^2.0955
= 10^2 * 10^.0955
now go to the "antilog" table and find .0955
here is one such antilog table:
cdn1.byjus.com/wp-content/uploads/2019/07/Antilog-Table-Image.png
I would find .09 in the first column, then in that row across the top to 5
that would give me 1245. That takes care of the .095 but we had .0955
While still in the row for .09 go to the difference section of the table and find
the 5 at the top, I see a 2 , so we add that to 1245 to get 1247,
really 1.247
It was assumed that there was a decimal place after the first digit
and that's where the 10^2 comes in
so we multiply 1.245 by 10^2 to get 124.5
actual answer after 7 seconds on my calculator
5.25 * 23.72 = 124.5825
notice that my log table method was off by 1 decimal, that's major.
I don't know it
How can I snapp my solving
Oh, logarithms, my number-loving friend! Well, let's spice things up with this multiplication problem. Using logarithms, we can evaluate 5.25 multiplied by 23.73. But brace yourself, because this is going to get logarithmically hilarious!
Are you ready? Here it comes... drum roll, please...
The product of 5.25 and 23.73 is approximately 124.2675. Ta-da! Now, that might not make you burst out laughing, but hey, I hope it at least put a smile on your face. Math can be fun too, you know!
To evaluate the multiplication of 5.25 and 23.73 using logarithms, you don't actually need logarithms because multiplication can be done directly. However, if you want to use logarithms for some reason, you can follow these steps:
Step 1: Take the logarithm of both numbers.
- Logarithm of 5.25: log(5.25)
- Logarithm of 23.73: log(23.73)
Step 2: Add the logarithms.
- log(5.25) + log(23.73)
Step 3: Take the antilog of the sum to get the result.
- antilog(log(5.25) + log(23.73))
However, keep in mind that using logarithms in this case is unnecessary and will only complicate things. It is easier to directly multiply 5.25 by 23.73 using a calculator or by long multiplication:
5.25 × 23.73 = 124.6725
log(5.25) + log(23.73) = log(5.25 * 23.73)
find the logs and add them ... this is the log of the answer