Question

Calculate anti logarithms:
It is inverse log calculation or exponentiation.
$100$ is the antilogarithm of $2$ to base $10$ , known as antilog.
Ex:
Antilog (-8.654), using an Anti-logarithmic table.

Answer 1

Hint: Antilog is the inverse function of log. Thus an antilog functions to exponentiate a simplified log value. To compute the antilogarithm of a number y, you must raise the logarithm base b (usually $10$ , sometimes the constant $e$) to the power that will generate the number y. Both logarithm and antilogarithm have their base as $2.7183$ . If the logarithm and antilogarithm are having their base $10$ , that should be converted into natural logarithms and antilog by multiplying it by $2.303$ .

Complete answer: A number has two parts. The Characteristic part and the Mantissa part.
Characteristic Part – The whole part of the number is called the Characteristic part.
Mantissa Part – The decimal part of the logarithm number for a given number is called the Mantissa part, and it should always be a positive value. If the mantissa part is a negative value, convert it into the positive value.

The first step is to separate the characteristic and mantissa part. In the given number, $ - 8.654$, the characteristic part is $ - 8$ and the mantissa part is $ - 0.654$ .
The second step is to convert the negative value into positive. We do this by subtracting $1$ from tha characteristic part and adding $1$ to the mantissa part as follows:
 $ - 8 - 1 = 9$ and $ - 0.654 + 1 = 0.346$
Now we have to find the antilog of $0.346$ as follows:
Taking the value corresponding to row $.34$ and column $6$ , we get $2218$
Thus we write $0.2218$
Now we take the Characteristic part, say $n$ and multiply $0.2218$ with ${10^n}$
Here, $n = - 9$ and so the antilog of the given number is $0.2218 \times {10^{ - 9}}$

Note:
In case there was another decimal place after $0.654$ we would have considered the mean difference value corresponding to the row $.34$ and the mean difference column of that value. That value would then be added to $.2218$ and then multiplied by ${10^{ - 9}}$.