Question

How do you simplify ${e^{3\ln x}}$ ?

Answer 1

In order to determine the value of the above question ,use logarithmic property $n\log m = \log {m^n} \\\ {m^{\log (n)}} = n \\\$ .
Formula:
$n\log m = \log {m^n} \\\ {m^{\log (n)}} = n \\\$

Complete step by step solution:
To solve the given question, we must know the properties of logarithms and with the help of them we are going to rewrite our question.
But we also need to know that the number $e$ and $\log n$ are actually inverses of each other.

First, we are going to rewrite the number with the help of the following properties of natural logarithms.
$n\log m = \log {m^n} \\\ {e^{\log (n)}} = n \\\$
So,
$= {e^{3\ln x}} \\\ = {e^{\ln ({x^3})}} \\\ = {x^3} \\\$

Therefore ,simplification of ${e^{3\ln x}}$ is ${x^3}$ .

Note:
1. Value of the constant ”e” is equal to 2.71828.
2. A logarithm is basically the reverse of a power or we can say when we calculate a logarithm of any number , we actually undo an exponentiation.