Question

what is the value of (e^{ln 7x})?

• 1
• 7e
• 7x
• 7

Explanation:

⚡ Using what you learned: properties of logarithms

Step 1: Identify the inverse property

The expression is of the form:

$$ e^{\ln(u)} $$

Since the natural exponential function \( e^x \) and the natural logarithmic function \( \ln(x) \) are inverse functions, they undo each other:

$$ e^{\ln(u)} = u $$

Step 2: Simplify the expression

Substitute \( u = 7x \) into the identity:

$$ e^{\ln(7x)} = 7x $$

Answer:

\( 7x \)