Isolating and Solving Exponential Equations: A Step-by-Step Guide to Find Solutions.

What is the solution to4 + 5e^(x+2) = 11

A.

To find the solution to the equation 4 + 5e^(x+2) = 11, we need to isolate the exponential term on one side of the equation and then solve for x.

Step 1: Subtract 4 from both sides of the equation:

5e^(x+2) = 7

Step 2: Divide both sides of the equation by 5:

e^(x+2) = 7/5

Step 3: Take the natural logarithm of both sides of the equation:

ln(e^(x+2)) = ln(7/5)

Using the rule that ln(e^a)=a, we can simplify the left side of the equation:

x+2 = ln(7/5)

Step 4: Subtract 2 from both sides of the equation:

x = ln(7/5) – 2

This is the solution to the equation 4 + 5e^(x+2) = 11. We can also use a calculator to find a numerical approximation for the solution:

x ≈ -0.263

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