Question

How do you write the exponential notation for ${{\log }_{2}}4096=12$ ?

Answer 1

Hint: Here in this question we have been asked to write the exponential notation for given the logarithmic expression ${{\log }_{2}}4096=12$ . From the basic definition of logarithm we know that for any exponential function given as ${{a}^{x}}=y$ the logarithmic function is expressed as ${{\log }_{a}}y=x$ . We will use this definition in order to answer this question.

Complete step by step answer:
Now considering from the question we have been asked to write the exponential notation for the given logarithmic expression ${{\log }_{2}}4096=12$ .
From the basic definition of the logarithm which we have learnt during the basics of logarithms we know that for any exponential function given as ${{a}^{x}}=y$ the logarithmic function is expressed as ${{\log }_{a}}y=x$ .
By using this definition here in this solution process. By comparing the given logarithmic expression and the expression in the logarithmic definition we will get $a=2$ , $y=4096$ and $x=12$ .

Therefore the exponential notation for the given logarithmic expression ${{\log }_{2}}4096=12$ will be given as ${{2}^{12}}=4096$ .

Note: While answering questions of this type we should be sure with the logarithmic concepts that we are going to apply in between the process. This is a very simple and easy question and can be answered accurately in a short span of time. Very few mistakes are possible in questions of this type. If we had confused with the definition and written it as ${{\log }_{a}}x=y\Rightarrow {{a}^{x}}=y$ then we will have the answer as ${{\log }_{2}}4096=12\Rightarrow {{2}^{4096}}=12$ which is a wrong answer clearly.