How do you use log tables to find logarithm and the antilogarithm of $445.66$ ?

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Answer 1 · 2017-05-25T06:34:07

$log 445.66 ~~ 2.6490$

$10^445.66 ~~ 4.571 xx 10^445$

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Log of $445.66$

In the log table, find the row for numbers beginning $44$ and examine the columns for $5$ and $6$ .

They will contain numbers like $6484$ and $6493$ respectively.

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Then since $445.66$ is about $2/3$ of the way between $445$ and $446$ , we add $(6493-6484)*2/3 = 6$ to $6484$ to get $6490$

Hence the logarithm of $4.4566$ is approximately $0.6490$

Then:

$log(445.66) = log(100*4.4566)$

$= log(100)+log(4.4566) ~~ 2+0.6490 = 2.6490$

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Antilog of $445.66$

In the antilog table against $0.66$ in the $0$ column, we find something like $4571$

That tells us that $10^0.66 ~~ 4.571$

Hence:

$10^445.66 ~~ 4.571 xx 10^445$

How do you use log tables to find logarithm and the antilogarithm of 445.66445.66 ?