Question

How do you evaluate \[{e^{\ln 3}}\]?

Answer 1

Hint: In the given question, we have been given an expression. It is an expression of natural logarithm. In this question, we have been given the constant Euler’s number which is raised to the natural logarithm.We have to simplify the expression. We can easily do that if we know the properties of logarithm.

Formula Used:
In the given question we are going to use the formula:
\[{e^{\ln nx}} = nx\]

Complete step by step solution:
In the given question, we have been given the expression,
\[{e^{\ln 3}}\]
In the given question we are going to use the formula:
\[{e^{\ln nx}} = nx\]
So, substituting the value in the formula of \[nx = 3\], we have,
\[{e^{\ln 3}} = 3\]
Hence, the answer to the question is \[{e^{\ln 3}} = 3\].

Additional Information: The \[\log \] function has other basic properties too:
\[{\log _x}{x^n} = n\]
\[{\log _b}a = n \Rightarrow {b^n} = a\]
\[{\log _a}b = \dfrac{1}{{{{\log }_b}a}}\]

Note: In the given question, we had to solve the given expression containing an expression involving the use of Euler’s constant and the natural log function. The natural log function is a special case of the logarithm function with the base of Euler’s constant. The place where some students get stuck is when they do not know the meaning of the natural log function, and when they do not know the formula of the logarithm functions; without knowing the formula of this concept, it is impossible to solve the question. So, we need to remember the required formula so that we can solve this question.