Question

question 17
$e^{ln 9x^3}$
○ 3
○ $9x^3$
○ $e^{9x^3}$
○ $ln 9x^3$

Explanation:

Step1: Recall the inverse property of exponential and logarithmic functions.

The exponential function \( e^x \) and the natural logarithmic function \( \ln x \) are inverse functions of each other, which means for any positive real number \( a \), \( e^{\ln a}=a \).

Step2: Apply the inverse property to the given expression.

In the expression \( e^{\ln 9x^3} \), we can let \( a = 9x^3 \) (assuming \( 9x^3>0 \), which is valid for the domain where the natural logarithm is defined). Using the property \( e^{\ln a}=a \), we substitute \( a = 9x^3 \) into the property, so \( e^{\ln 9x^3}=9x^3 \).

Answer:

\( 9x^3 \) (corresponding to the option with text "9x³")