Question

How do you solve $\ln {{e}^{2}}$ ?

Answer 1

Hint: The function $y={{e}^{x}}$ and $y=\ln x$are inverse functions. To solve this problem, we need to know the logarithmic and radical property which is $\ln {{a}^{b}}=b\ln a$.

Complete Step By Step solution:
According to the given information, we have to solve $\ln {{e}^{2}}$.
We know that the natural log ($\ln $) and the exponential function (${{e}^{x}}$) are inverses of each other which simply means that they will cancel out each other resulting in $1$.
The given question is, $\ln {{e}^{2}}$
Using the property $\ln {{a}^{b}}=b\ln a$ we can write it as,
$2\ln e$
In this case, if I know that as $\ln $ and $e$ are inverse of each other, they will simply undo each other.

Hence the result will be $=2$.

Note:
We know that the natural log ($\ln $) and the exponential function (${{e}^{x}}$) are inverses of each other, which means that if we raise the exponential function by $\ln $ of $x$, we would be able to find $x$. But remember, if something is done on one side of the equation, the same thing has to happen on the opposite side of the equation too.