Question

what is the value of $e^{ln 7x}$?
○ 1
○ 7e
○ 7x
○ 7

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. By the property of inverse functions, for any positive real number \( a \), we have \( e^{\ln(a)} = a \).

Step2: Apply the property to the given expression

In the expression \( e^{\ln(7x)} \), we can let \( a = 7x \) (assuming \( 7x>0 \), i.e., \( x > 0 \) since the natural logarithm is only defined for positive numbers). Using the property \( e^{\ln(a)}=a \), we substitute \( a = 7x \) into the formula. So \( e^{\ln(7x)}=7x \).

Answer:

\( 7x \) (corresponding to the option "7x")