asking to solve a logarithmic problem: ln(x + 3) = 2
user
To solve the equation \(\ln(x + 3) = 2\), we start by rewriting the equation in its exponential form:

\[
e^2 = x + 3
\]

Next, we solve for \(x\) by subtracting 3 from both sides:

\[
x = e^2 - 3
\]

Thus, the solution is:

\[
x = e^2 - 3
\]

If you need the numerical value, \(e^2 \approx 7.389\), so:

\[
x \approx 7.389 - 3 = 4.389
\]

The final answer is:

\[
x \approx 4.389
\]
assistant
follow up: what is the numerical value of e^2?
user
The numerical value of \(e^2\) is approximately \(7.389\).
assistant
giving another logarithmic problem: 2 log_3(4x) = 4
user
To solve the equation \(2 \log_3(4x) = 4\), we first simplify by dividing both sides by 2:

\[
\log_3(4x) = 2
\]

Next, we rewrite the logarithmic equation in its exponential form:

\[
4x = 3^2
\]

This simplifies to:

\[
4x = 9
\]

Finally, we solve for \(x\) by dividing both sides by 4:

\[
x = \frac{9}{4} = 2.25
\]

So, the solution is:

\[
x = 2.25
\]
assistant