MHB Finding the log by using the proportional table

AI Thread Summary
To find the logarithm of 29517, the discussion utilizes a proportional table. By referencing row 295, the value 46997 is identified, and an additional value of 11.2 is added based on the second table for the last digit. This results in a total of 47008.2, which is interpreted as 0.470082 when decimal points are considered. The final logarithm value is calculated as 4.470082, with a minor discrepancy noted when compared to a calculator's output.
cbarker1
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MHB
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Logarithms​
[TABLE="class: outer_border, width: 500, align: left"]
[TR]
[TD]N[/TD]
[TD]0[/TD]
[TD]1[/TD]
[TD]2[/TD]
[/TR]
[TR]
[TD]293[/TD]
[TD]46687[/TD]
[TD]46702[/TD]
[TD]46716[/TD]
[/TR]
[TR]
[TD]294[/TD]
[TD]46850[/TD]
[TD]46835[/TD]
[TD]46864[/TD]
[/TR]
[TR]
[TD]295[/TD]
[TD]46982[/TD]
[TD]46997[/TD]
[TD]47012[/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[/TABLE]
Prop. Pts​

[TABLE="class: grid, width: 500, align: right"]
[TR]
[TD]1[/TD]
[TD]1.6[/TD]
[/TR]
[TR]
[TD]2[/TD]
[TD]3.2[/TD]
[/TR]
[TR]
[TD]3[/TD]
[TD]4.8[/TD]
[/TR]
[TR]
[TD]4[/TD]
[TD]6.4[/TD]
[/TR]
[TR]
[TD]5[/TD]
[TD]8.0[/TD]
[/TR]
[TR]
[TD]6[/TD]
[TD]9.6[/TD]
[/TR]
[TR]
[TD]7[/TD]
[TD]11.2[/TD]
[/TR]
[TR]
[TD]8[/TD]
[TD]12.8[/TD]
[/TR]
[TR]
[TD]9[/TD]
[TD]14.4[/TD]
[/TR]
[/TABLE]

Find the value of $\log\left({29517}\right)$
Work:
4+$\log\left({2.9517}\right)$

Thanks for your help
 
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Cbarker1 said:
Logarithms​
[TABLE="class: outer_border, width: 500, align: left"]
[TR]
[TD]N[/TD]
[TD]0[/TD]
[TD]1[/TD]
[TD]2[/TD]
[/TR]
[TR]
[TD]293[/TD]
[TD]46687[/TD]
[TD]46702[/TD]
[TD]46716[/TD]
[/TR]
[TR]
[TD]294[/TD]
[TD]46850[/TD]
[TD]46835[/TD]
[TD]46864[/TD]
[/TR]
[TR]
[TD]295[/TD]
[TD]46982[/TD]
[TD]46997[/TD]
[TD]47012[/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[/TABLE]
Prop. Pts​

[TABLE="class: grid, width: 500, align: right"]
[TR]
[TD]1[/TD]
[TD]1.6[/TD]
[/TR]
[TR]
[TD]2[/TD]
[TD]3.2[/TD]
[/TR]
[TR]
[TD]3[/TD]
[TD]4.8[/TD]
[/TR]
[TR]
[TD]4[/TD]
[TD]6.4[/TD]
[/TR]
[TR]
[TD]5[/TD]
[TD]8.0[/TD]
[/TR]
[TR]
[TD]6[/TD]
[TD]9.6[/TD]
[/TR]
[TR]
[TD]7[/TD]
[TD]11.2[/TD]
[/TR]
[TR]
[TD]8[/TD]
[TD]12.8[/TD]
[/TR]
[TR]
[TD]9[/TD]
[TD]14.4[/TD]
[/TR]
[/TABLE]

Find the value of $\log\left({29517}\right)$
Work:
4+$\log\left({2.9517}\right)$

Thanks for your help

Hi Cbarker1,

To find $\log(2.9517)$, we look up row $295$ in the table.
Then we pick the column with 1, where we find $46997$.
For the last digit we consult the 2nd table, where entry $7$ has $11.2$, which we add for a total of $47008.2$.

In the table the decimal points have been left out, which means we need to read this as $0.470082$.
Add the $4$ you found for a total of $4.470082$.

My calculator says $4.470072$.
Presumably the small discrepancy is an approximation error due to the use of the second table.
 

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