Question

evaluate or simplify the expression without using a calculator.
$e^{\ln 114}$
$e^{\ln 114}=\square$

Explanation:

Step1: Recall inverse property of exponential and logarithmic functions

The exponential function \( e^x \) and the natural logarithmic function \( \ln x \) (which is \( \log_e x \)) are inverse functions of each other. For any positive real number \( a \), the property \( e^{\ln a}=a \) holds because applying an inverse function to its original function cancels out the operation.

Step2: Apply the property to the given expression

In the given expression \( e^{\ln 114} \), we can identify that \( a = 114 \) (since \( 114>0 \), it satisfies the domain requirement for the natural logarithm). Using the property \( e^{\ln a}=a \), we substitute \( a = 114 \) into the property. So \( e^{\ln 114}=114 \).

Answer:

\( 114 \)