Question

evaluate or simplify the expression without using a calculator.
$e^{ln 119}$

$e^{ln 119} = \square$

Explanation:

Step1: Recall the inverse property of exponential and logarithmic functions

The natural logarithm function \(\ln(x)\) is the inverse of the exponential function \(e^x\). By the inverse property of functions, for any positive real number \(a\), we have \(e^{\ln(a)} = a\).

Step2: Apply the inverse property to the given expression

In the given expression \(e^{\ln(119)}\), we can see that \(a = 119\) (and \(119>0\) which satisfies the domain requirement for the natural logarithm). So, using the inverse property \(e^{\ln(a)} = a\) with \(a = 119\), we get \(e^{\ln(119)}=119\).

Answer:

\(119\)