Using Logartihm Table

[Guest]

Multiply 35 * 75 using logarithm tables.

Not sure how to proceed.

[Baltuilhe]

Hi!

[tex]E=35\times 75\\
\log\;E=\log\left(35\times 75\right)\\
\log\;E=\log\;35+\log\;75\\
\log\;E=1,54407+1,87506\\
\log\;E=3,41913\\
E=10^3,41913\\
E=10^3\times 10^0,41913\\
E=1\,000\times 0,2625\\
E=2625[/tex]

Look for 35 and 75

Captura de Tela 2019-10-30 às 23.17.31.png (538.45 KiB) Viewed 1360 times

Look for 0,41913

Captura de Tela 2019-10-30 às 23.26.41.png (818.71 KiB) Viewed 1360 times

[Guest]

Thanks.

A question:

How would the log be determined if not in the table ?

[Baltuilhe]

Hi!!!

You can look for all numbers in a complete table. I've just pasted a part of it
https://archive.org/details/logarithmictrigo00hedriala/page/xvi

[Guest]

Ok, Thanks again!

[Guest]

A follow-up question;

In the book link provided, example to find 72054 (not in table);

72050 = 4.85763

72060 = 4.85769

Difference = 0.00006

A change of 4 in number is 0.4 * 0.00008 = 0.00002
My question: Is the "4" used from the last digit in 72054 ?

[Baltuilhe]

A follow-up question;

In the book link provided, example to find 72054 (not in table);

72050 = 4.85763

72060 = 4.85769

Difference = 0.00006

A change of 4 in number is 0.4 * 0.00006 = 0.00002
My question: Is the "4" used from the last digit in 72054 ?

The number 6 in red was to fix a possible mistake, right?
But the 4 used is the last digit, you're right!

But you don't need to do this account.
See:

700 - Logarithms of Numbers

Captura de Tela 2019-11-03 às 00.42.38.png (380.98 KiB) Viewed 1327 times

In the table has a auxiliary table with 7 and 6 (the difference between two given logs).
In the case, we want 72054, right?
72050 => 85763
72060 => 85769
The difference is 6, right?
But we want a new digit of 4, right?
So, in the table column 6, line 4, you have 2.4

85763+2.4=85765.4

Now you can give the log:
log 72054 = 4,857654, ok?

Try another values!

[Guest]

Log of 6484.

log 6480 = 1158

log 6490 = 1124

Difference of 6480 and 6490 = 10

Difference of 1158 and 1125 = 34

I think I used the wrong numbers. Some confused about the tables.

[Guest]

Please reply, Thanks.

[Baltuilhe]

Log of 6484.

log 6480 = 1158

log 6490 = 1124

Difference of 6480 and 6490 = 10

Difference of 1158 and 1125 = 34

I think I used the wrong numbers. Some confused about the tables.

log 6484 = 3+0,81184=3,81184, directly!

[Guest]

Thanks again!