Question

evaluate or simplify the expression without using a calculator.
$e^{ln 133}$
$e^{ln 133} = \square$

Explanation:

Step1: Recall the inverse property of exponential and logarithmic functions

The natural logarithm function $\ln(x)$ is the inverse of the exponential function $e^x$. For any positive real number $a$, the property $e^{\ln a}=a$ holds because applying an exponential function and its inverse logarithm function (or vice versa) cancels out the operation.

Step2: Apply the property to the given expression

In the expression $e^{\ln 133}$, we can see that $a = 133$ (and $133>0$, so the property is applicable). Using the property $e^{\ln a}=a$, we substitute $a = 133$ into the formula. So $e^{\ln 133}=133$.

Answer:

133