Respuesta :
The number raised with logarithm with base of that number cancels out.
Thus, the value of [tex]e^{ln(7x)}[/tex] will be given by:
Option C: 7x
Given that:
To evaluate the expression: [tex]e^{ln(7x)}[/tex]
What is natural logarithm?
Natural logarithm is logarithm with base e. e is not a variable but a special mathematical constant. e = 2.7182818....
When logarithm has base as e, then we write it as ln instead of log. It is called natural logarithm
[tex]e^a = b \implies a = ln(b)[/tex]
Thus, let [tex]e^{ln(7x)} = b[/tex]. Then we will have:
[tex]e^{ln(7x)} = b\\ln(7x) = ln(b)\\b = 7x \text{\: (since ln(x) is a one to one function)}\\\\\: \rm Thus,\\\\e^{ln(7x)} = b = 7x[/tex]
Thus, Option C: 7x is correct value of [tex]e^{ln(7x)}[/tex].
Learn more about natural logarithm here:
https://brainly.com/question/305900
