\[
\begin{array}{r}
2 e^{x}-3=1 \\
2 e^{x}=4 \\
e^{x}=2
\end{array}
\]
What is the next step when solving the equation $2 \mathrm{e}^{\mathrm{x}}-3=1$ ?

Answer

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Answer

$\boxed{x = \ln(2)}$

Steps

Step 1 ：The next step in solving the equation $2e^x - 3 = 1$ is to add $3$ to both sides of the equation to get $2e^x = 4$.

Step 2 ：Then, divide both sides of the equation by $2$ to isolate $e^x$, which gives $e^x = 2$.

Step 3 ：Finally, take the natural logarithm of both sides to solve for $x$, which gives $x = \ln(2)$.

Step 4 ：$\boxed{x = \ln(2)}$