To evaluate the expression [tex]\(\ln(e^e)\)[/tex], we can use properties of logarithms. Specifically, the natural logarithm function, denoted as [tex]\(\ln(x)\)[/tex], has the property that [tex]\(\ln(a^b) = b \cdot \ln(a)\)[/tex].
Here’s the expression we need to evaluate:
[tex]\[
\ln(e^e)
\][/tex]
Using the logarithm property [tex]\(\ln(a^b) = b \cdot \ln(a)\)[/tex], we get:
[tex]\[
\ln(e^e) = e \cdot \ln(e)
\][/tex]
Now, the natural logarithm of [tex]\(e\)[/tex] (where [tex]\(e\)[/tex] is Euler's number, approximately equal to 2.718) is 1:
[tex]\[
\ln(e) = 1
\][/tex]
Substituting this back into our expression, we have:
[tex]\[
\ln(e^e) = e \cdot 1 = e
\][/tex]
Thus, the value of the expression [tex]\(\ln(e^e)\)[/tex] is [tex]\(e\)[/tex], which corresponds to option C.
So, the correct answer is:
[tex]\[
\boxed{C}
\][/tex]
