To simplify the expression \(\ln(e^{2x})\), you can use the property of logarithms that states:
\[ \ln(a^b) = b \cdot \ln(a) \]
In this case, \(a = e\) and \(b = 2x\). Therefore, you can apply the property as follows:
\[ \ln(e^{2x}) = 2x \cdot \ln(e) \]
From the properties of logarithms, we know:
\(\ln(e) = 1\).
So we can substitute that in:
\[ \ln(e^{2x}) = 2x \cdot 1 = 2x. \]
Thus, the simplified expression is:
\[ \ln(e^{2x}) = 2x. \]