Question

If \[x = {\log _a}m\] , then value of \[m\] is equal to
A. \[anti{\log _a}x\]
B. \[anti{\log _x}a\]
C. \[{a^x}\]
D. \[{x^a}\]

Answer 1

Hint: To solve the above question of logarithm, we can follow two methods. In the first method we can use antilogarithm and in the second method we can use \[e\] on both the sides of the equation. As a result of two different methods of solving the equation, the above question will have two answers.

Formula used: To solve the above question, you have to keep in mind that \[{e^{{{\log }_a}x}} = x\] .

Complete step by step solution:
We are given that \[x = {\log _a}m\] .
Now we will use two different methods to solve the above question.
Method.
We know that \[{e^{{{\log }_a}x}} = x\] ,
We have, \[x = {\log _a}m\] ,
We can write this as:
 \[
   \Rightarrow {a^x} = {a^{{{\log }_a}m}} \\
   \Rightarrow {a^x} = m \\
 \] .
Therefore, one of our answers is \[{a^x} = m\] .
So, our first option is C. \[{a^x} = m\] .
Now,
Method.
In this method, we will use the antilogarithm. It is an inverse technique which used to calculate the logarithm of the same number.
We are given \[x = {\log _a}m\] ,
In antilog we will raise the base being used to the logarithm given.
Therefore, through this method we get, \[m = anti{\log _a}x\] .
So, our second option is A. \[m = anti{\log _a}x\] .

So, the correct answer is Option A.

Note: To evaluate the answer of the above question, we have used two different methods and the answer from both the methods is different. While solving such questions, make sure you show the working of all the methods applicable and choose all the suitable options from the multiple choices.