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Solve for x in the following equation. Leave your answer in terms of the natural log, ln.

2e^(x-4) = 11

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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.

User Samuel Chen
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