Change of bases with log tables

[cbarker1]

Hi everyone,

I need some help to solve this problem:

The direction states to find the value by using the log table

$\log_{3}\left({825.6}\right)$

Work:

I using the change of base:
$\log_{3}\left({825.6}\right)=\frac{\log\left({825.6}\right)}{\log\left({3}\right)}$

I look up the values of the logarithm of 3 and 825.6.

$\log\left({825.6}\right)=.91677+2$ =$\log\left({8.256}\right)+2$

$\log\left({3}\right)=.47712$

yields

$\log_{3}\left({825.6}\right)=\frac{2.91677}{.47712}$

Taking the log of both sides:
$\log\left({\log_{3}\left({825.6}\right)}\right)=\log\left({\frac{2.91677}{.47712}}\right)$

Using the log identity to dividing to difference:
$\log\left({\log_{3}\left({825.6}\right)}\right)=\log\left({2.91677}\right)-\log\left({.47712}\right)$

Finding the values of log(2.91677) and log(.47712)

Do I drop the last digit in (2.91677 and .47712) and look up the first four digits or do I interpolate the last digits by using the Table of proportional parts?

Thank you,

Cbarker

 

[Ackbach]

Sorry, I'm a bit confused. What exactly are you being asked to compute?

 

[cbarker1]

Compute the value by using log table
$\log_{3}\left({825.6}\right)$

 

[MarkFL]

I think I would observe:

\(\displaystyle 825.6=\frac{2^6\cdot3\cdot43}{10}\)

And now apply some log properties, and then use the change of base as needed. :D