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

May 25, 2017

$\log 445.66 \approx 2.6490$

${10}^{445.66} \approx 4.571 \times {10}^{445}$

#### Explanation:

$\textcolor{w h i t e}{}$
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.

Then since $445.66$ is about $\frac{2}{3}$ of the way between $445$ and $446$, we add $\left(6493 - 6484\right) \cdot \frac{2}{3} = 6$ to $6484$ to get $6490$

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

Then:

$\log \left(445.66\right) = \log \left(100 \cdot 4.4566\right)$

$= \log \left(100\right) + \log \left(4.4566\right) \approx 2 + 0.6490 = 2.6490$

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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 ${10}^{0.66} \approx 4.571$

Hence:

${10}^{445.66} \approx 4.571 \times {10}^{445}$