evaluate the expression without the use of a calculator. in1 in1 = (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the definition of natural - logarithm

The natural - logarithm $\ln x$ is the inverse of the exponential function $y = e^{x}$. That is, if $y=\ln x$, then $x = e^{y}$.

Step2: Set up the equation for $\ln1$

Let $y=\ln1$. By the definition of the natural - logarithm, we have $e^{y}=1$.

Step3: Solve for $y$

We know that for the exponential function $y = e^{x}$, when $x = 0$, $e^{0}=1$. So, if $e^{y}=1$, then $y = 0$.

Answer:

$0$