Question

simplify.
$e^{ln x} = square$
$e^{ln 5} = square$
$e^{ln 3x} = square$

Explanation:

Step1: Recall Inverse Property of Exponential and Logarithm

The exponential function \( e^x \) and the natural logarithm function \( \ln x \) are inverse functions, so \( e^{\ln a}=a \) for any positive real number \( a \).

Step2: Simplify \( e^{\ln x} \)

Using the inverse property \( e^{\ln a}=a \), when \( a = x \) (assuming \( x>0 \)), we have \( e^{\ln x}=x \).

Step3: Simplify \( e^{\ln 5} \)

Using the same inverse property \( e^{\ln a}=a \), when \( a = 5 \), we get \( e^{\ln 5}=5 \).

Step4: Simplify \( e^{\ln 3x} \)

Using the inverse property \( e^{\ln a}=a \), when \( a = 3x \) (assuming \( 3x>0 \) or \( x > 0 \)), we have \( e^{\ln 3x}=3x \).

Answer:

\( e^{\ln x}=\boldsymbol{x} \)

\( e^{\ln 5}=\boldsymbol{5} \)

\( e^{\ln 3x}=\boldsymbol{3x} \)