Question

If \[\log 3=0.47712\] then the value of \[antilog\left( 0.47712 \right)\]
(a) 0.3
(b) 0.03
(c) 3
(d) 1.4

Answer 1

Hint: In this question, from the relation between the logarithm and antilogarithm we can get the relation between the given two equations. Then apply antilogarithm on both sides of the given equation and rearrange the terms and simplify further to get the result.

Complete step-by-step answer:
First we define logarithm and antilogarithm
Logarithm:If a is a positive real number other than 1 and \[{{a}^{x}}=m\], then x is called the logarithm of m to the base a, written as \[{{\log }_{a}}m\]. In this \[{{\log }_{a}}m\], m should be always positive.
The logarithm with base 10 is called the common logarithm.
Antilogarithm:The positive number a is called the antilogarithm of the number b, if a is antilogarithm of b, then we write \[a=anti\log b\].
So, \[a=anti\log b\Leftrightarrow \log a=b\]
Let us now apply this relation between logarithm and antilogarithm to the equation given in the question.
Now, from the given equation in the question we get,
\[\Rightarrow \log 3=0.47712\]
Now, by applying antilog on both the sides we can further write it as
\[\Rightarrow anti\log \left( \log 3 \right)=antilog\left( 0.47712 \right)\]
As we already know that by applying the antilogarithm to a logarithm term then its logarithm will be removed on doing so.
Now, the above equation will be further simplified as.
\[\Rightarrow antilog\left( 0.47712 \right)=3\]
Hence, the correct option is (c).

Note: Instead of applying antilog on both the sides we can directly convert the given logarithm term to the antilogarithm term using the relation between both of them or also we can apply the logarithm to the asked value and then substitute the given value in it. Both the methods give the same result.It is important to note that as the given number or the number to which we need to find the antilogarithm are positive. So, we can directly get the values by applying the corresponding relation.