How reliable are logarithm tables?

• B
Today I came across a high school math book which has a particular problem in the logarithms chapter. It has
$$\log_{10}{0.2913} = -1.4643$$
Trying to verify it with a calculator, I get -0.53566. There's a log table attached at the end which agrees with the calculation made in the book. To make sure there wasn't a typo, I looked up online for the common logarithm table and found tables that agree with it. Trying to verify the book's calculation, I got (with a calculator)
$$10^{-1.4643} = 0.034332$$
Now am I missing something or is it something wrong with the logarithm tables I have? Admittedly, it has been a very long time since I last calculated logarithms using a table.

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mfb
Mentor
That is a very odd error, as it is off by nearly (but not exactly) 1. Are the logarithm values next to it wrong in a similar way?
Does your logarithm table really have exactly this entry?

It is off for the next value in the same problem too. It calculates $$\log_{10}{0.004236}$$ as -3.6269 while with a calculator I get -2.373044.
Even weirder is that it proceeds to add the two logarithms (which it calculated as -1.4643 and -3.6269) to get -3.0912. Then it proceeds to take the anti-log of -3.0912 and gets 0.001234 (while with a calculator I get $$10^{-3.0912} = 0.0008106$$). At this point I stopped taking the book seriously but thought I'd make sure whether it's a problem with me or the book before I explain it to my friend.

Nidum
Gold Member
It's written in what we called 'bar' notation in school .

Roughly : number of decade shifts + basic log of number in range 1 to 10

0.4643 is the log of 2.913

log of 0.2913 = -1 + 0.4643 = - 0.5357

You can see why this works :

log 0.2913 = log 2.913 - log 10

It's written in what we called 'bar' notation in school .

Roughly : number of decade shifts + basic log of number in range 1 to 10

0.4643 is the log of 2.913

log of 0.2913 = -1 + 0.4643 = - 0.5357

You can see why this works :

log 0.2913 = log 2.913 - log 10
Oh. So the bar isn't actually a negative? Why would they decide to write it this way?

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Are there cases where the bar notation is useful other than confusing poor unsuspecting readers?

Nidum
Gold Member
It greatly reduces the number of log values that are needed in tables . All you need are logs for numbers in range 1 to 10 .

There are also some small advantages in making calculations more systematic and in reducing chance of order of magnitude errors in final answers .