Solve the equation e^2x = 10.

The solution to e^2x = 10 is x = ln(5)/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(10)

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

2x ln(e) = ln(10)

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

2x = ln(10)

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

x = ln(10)/2

We can simplify this expression further by using the fact that ln(10) = ln(5*2) = ln(5) + ln(2):

x = (ln(5) + ln(2))/2

Since ln(2) is a constant, we can simplify this expression to:

x = ln(5)/2

Therefore, the solution to e^2x = 10 is x = ln(5)/2.