Answer: second option.
Step-by-step explanation:
In order to solve this exercise, it is necessary to remember the following properties of logarithms:
[tex]1)\ ln(p)^m=m*ln(p)\\\\2)\ ln(e)=1[/tex]
In this case you have the following inequality:
[tex]e^x>14[/tex]
So you need to solve for the variable "x".
The steps to do it are below:
1. You need to apply [tex]ln[/tex] to both sides of the inequality:
[tex]ln(e)^x>ln(14)[/tex]
2. Now you must apply the properties shown before:
[tex](x)ln(e)>ln(14)\\\\(x)(1)>2.63906\\\\x>2.63906[/tex]
3. Then, rounding to the nearest ten-thousandth, you get:
[tex]x>2.6391[/tex]
