Solve for x e^(x+6)=8

Problem

e(x+6)=8

Solution

1. Apply the natural logarithm to both sides of the equation to isolate the exponent.

ln(e(x+6))=ln(8)

2. Simplify the left side using the inverse property of logarithms, ln(eu)=u

x+6=ln(8)

3. Isolate x by subtracting 6 from both sides of the equation.

x=ln(8)−6

4. Rewrite the constant if needed, noting that ln(8)=ln(2)=3*ln(2) though the previous form is also standard.

x=3*ln(2)−6

Final Answer

x=ln(8)−6

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