Final answer:
To solve the equation 2e^(x-4) = 11, isolate the exponential term and then take the natural logarithm of both sides to cancel out the exponential function. The solution for x in terms of the natural logarithm, ln, is x = ln(11/2) + 4.
Step-by-step explanation:
To solve for x in the equation 2e^(x-4) = 11, we can start by isolating the exponential term on one side of the equation. Dividing both sides by 2 gives us e^(x-4) = 11/2. Next, we can take the natural logarithm (ln) of both sides of the equation to cancel out the exponential function. This gives us ln(e^(x-4)) = ln(11/2). Using the property ln(e^a) = a, we can simplify the equation to (x-4) = ln(11/2).
To solve for x, we can add 4 to both sides of the equation, resulting in x = ln(11/2) + 4. This is the solution for x in terms of the natural logarithm, ln.