Question

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

Answer 1

Find logarithm and the antilogarithm of $445.66$

In the log table, it contains numbers like $6484$and $6493$ respectively in the columns of $5$ and $6$ and $445.66$ is about $\frac{2}{3}$of the way between $445$ and $446$ .

Now add $\left(6493-6484\right)\times \frac{2}{3}=6$ to $6484$to get $6490$

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

Then $\log (445.66)=\log (100\times 4.4566)$

$$\begin{gathered} =\log \left(100\right)+\log (4.4566) \\ =2+0.6490 \\ =2.6490 \end{gathered}$$

Antilog of $445.66$ In the antilog table against $0.66$ in the $0$ columns, identify $4571$

That tell us ${10}^{0.66}=4.571$

Therefore,${10}^{445.66}=4.571\times {10}^{445}$

Hence the logarithm of$445.66$ is $2.6490$ and antilogarithm is $4.571\times {10}^{445}$