evaluate the following expression. you should do this problem without a calculator. e^ln 3 a. 1 b. 0 c. 3 d. 6
evaluate the following expression. you should do this problem without a calculator. e^ln 3 a. 1 b. 0 c. 3 d. 6
Answer
Explanation:
Step1: Recall logarithmic - exponential property
The functions $y = e^{x}$ and $y=\ln x$ are inverse functions of each other. That is, if $y = e^{x}$, then $x=\ln y$ and vice - versa. For any positive real number $a$, $e^{\ln a}=a$.
Step2: Apply the property to the given expression
In the expression $e^{\ln 3}$, by the inverse - function property of the exponential function $y = e^{x}$ and the natural logarithm function $y=\ln x$, we have $e^{\ln 3}=3$.
Answer:
C. 3