Solve the equation e^2x = 50.

The solution to e^2x = 50 is x = ln(25)/2.

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

ln(e^2x) = ln(50)

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

2x ln(e) = ln(50)

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

2x = ln(50)

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

x = ln(50)/2

We can simplify this expression further by using the property of logarithms that ln(a/b) = ln(a) - ln(b):

x = ln(50)/2 = (ln(25) + ln(2))/2 = ln(25)/2 + ln(2)/2

Therefore, the solution to e^2x = 50 is x = ln(25)/2.