Question

How do you write $\ln 0.2=x$ in exponential notation?

Answer 1

Here in this question we have been asked to write the exponential notation for given the logarithmic expression $\ln 0.2=x$ . 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 solution:
Now considering from the question we have been asked to write the exponential notation for the given logarithmic expression $\ln 0.2=x$ .
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 ${{\log }_{a}}y=x$ .
Here as it is given as $\ln$ that means it is a natural logarithm that indicates that it has base $e$ .
By comparing the given logarithmic expression and the expression in the logarithmic definition we will get $a=e$ and $y=0.2$.
Therefore the exponential notation for the given logarithmic expression $\ln 0.2=x$ will be given as ${{e}^{x}}=0.2$.

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 ${{\log }_{a}}y=x\Rightarrow {{a}^{y}}=x$ then we will have the answer as ${{\log }_{e}}0.2=x\Rightarrow {{e}^{0.2}}=x$ which is a wrong answer clearly.