# How can we find antilog using log table ? In the Example 3.2 in the NCERT, log KC= 15.6 For value of Antilog(15.6), how we have to proceed ? I don't know the basic logarithm too...Please tell which formula to apply ? Do we have to use log table ?

Dear Student,

You may refer to the answer posted by Sourabh Subhod. He has very well explained the answer.
Very good Sourabh. Keep it up!

Regards
Akanksha Jain

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same here
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log K= 15.6.
Here, the log of Kc is of base 10.
log of some number with the base 10 means the power to which 10 should be raised to get that number.
.In this case, we know the power to which 10 is raised to but we don't know the number it gives. That's where anti log comes into play.
antilog of a number = (the log base)the number
In this question, the number is 15.6 and the base is 10.
So, antilog(15.6) = 1015.6  = 100.6 * 1015 = antilog(0.6) * 1015

In 15.6, the part before the decimal point is called characteristic and the part after the decimal point
is called the matissa.
So in general,
antilog of a number = antilog(mantissa) * 10characteristic

Now use your log tables and go to the page for anitlogarithms.
Look for the row of 0.600
The value is 0,3981.
But we will be taking it as 3.981. [shift one decimal to the right]
So the final answer is antilog(15.6) = 3.981 * 1015
If you use a calculator and enter 1015.6, you'll get the same value as above.

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I actually forgot to add one more thing. It would be a different way to calculate the antilog of negative numbers. Suppose we have to find antilog of -15.6. The answer is 10-15.6. But the normal method has to be modified here. The easiest way is to split the power in such a way that you can use the rule am+n = a* an
Now do we split -15.6 like that?
-15.6 = -16+0.4.
In general, the negative number whose antilog is to be found can be splitted as :
the number = (characteristic - 1) + (1- mantissa)

So antilog(-15.6) = 10-15.6 = 10-16+0.4 = 10-16 * 100.4 = 10-16 * antilog(0.4)

Now we proceed as normal.
From log tables,
antilog value for 0.400 is given as 0.2512.
As usual, shift the decimal to the  right and the antilog of 0.4 is 2.512.
Hence, antilog(-15.6) = 2.512 * 10-16
Use this method only for finding antilog negative numbers. Use the first method for positive numbers.

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ThankYou Very Much ​Sourabh Subhod... :)
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What are you looking for?