Solve the equation e^2x = 7.

The solution to e^2x = 7 is x = ln(7)/2.

To solve this equation, we need to isolate x. We can do this by taking the natural logarithm of both sides:

ln(e^2x) = ln(7)

Using the property of logarithms that ln(a^b) = b ln(a), we can simplify the left-hand side:

2x ln(e) = ln(7)

Since ln(e) = 1, we can simplify further:

2x = ln(7)

Finally, we can solve for x by dividing both sides by 2:

x = ln(7)/2

Therefore, the solution to e^2x = 7 is x = ln(7)/2.