Question

Evaluate or simplify the expression without using a calculator.
ln e Superscript 2 x
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Part 1
ln e Superscript 2 xequals
  
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Answer 1

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:

\[
\ln(e^{2x}) = 2x.
\]