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The solution to the equation $\ln(2x) = 4$ is given by $x = \frac{e^4}{2}$.

To solve the equation $\ln(2x) = 4$, we first need to isolate the variable $x$. We accomplish this by exponentiating both sides of the equation with the base $e$, which is the base of the natural logarithm. This results in the following equation:

$e^{\ln(2x)} = e^4$

Utilizing the property of logarithms that states $\ln(e^a) = a$, we can simplify the left-hand side:

$2x = e^4$

Next, we isolate $x$ by dividing both sides of the equation by 2:

$x = \frac{e^4}{2}$

This expression can also be rewritten as:

$x = e^{2} \cdot e^{2} \cdot \frac{1}{2}$

However, it is more straightforward to present it as:

$x = \frac{e^4}{2}$

Thus, the final solution to the equation $\ln(2x) = 4$ is:

$x = \frac{e^4}{2}$.