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.