Question

How do you write \[{{\log }_{2}}16=4\] in exponential form?

Answer 1

Hint: To solve this question, we should have a proper knowledge in logarithms and also we should know how to convert logarithmic functions into exponential form. A logarithm is defined as the power to which a number must be raised to get some other values. First, we will know about the formula of which we are going to use in this question.

Complete step by step answer:
Let us solve the question.
As we know that some formulas are there in logarithms and exponents in which one of the formulas is \[{{\log }_{a}}{{a}^{n}}=n\] .
We are going to use this formula for solving this question.
Let us suppose, \[{{a}^{n}}=x\]
Then, we can say that
\[{{\log }_{a}}x=n\]
Or we can say that the logarithm of x to the base a is n.
Where x can be written as \[a\times a\times a\times a\times a\times a\times a..............n\text{ }times\] .
In other words, the logarithm gives the answer to the question “How many times a number is multiplied to get the other number?”
So, from the above lines, we can say that if \[{{\log }_{a}}x=n\] , then \[x={{a}^{n}}\] which is in exponential form.
In this question, we have asked to find the exponential form of \[{{\log }_{2}}16=4\] .

So, the exponential form will be \[16={{2}^{4}}\] .

Note: Nowadays, logarithms are used in the field of science and technology. They make the solving process of the questions or the calculations much easier at the time of solving questions. They are used in measuring the loudness (decibels), in radioactive decay, to find the acidity (pH=-log [H+]), etc.