Question

What is the answer to 5e2x - 4 = 11?

Answer 1

The equation 5e^2x - 4 = 11 is solved by isolating the exponential term and taking the natural logarithm of both sides, leading to the solution x = ln(3) / 2.

Step-by-step explanation:

To solve the equation 5e2x - 4 = 11, we need to isolate the exponential term and solve for x.

1. Add 4 to both sides of the equation to get 5e2x = 15.
2. Divide both sides by 5 to isolate the exponential term, resulting in e2x = 3.
3. Take the natural logarithm of both sides to obtain 2x = ln(3).
4. Finally, divide both sides by 2 to solve for x, which gives us x = ln(3) / 2.

Therefore, the solution to the equation is x = ln(3) / 2.