Solve for x 7-3e^(-x)=2

Problem

7−3*e(−x)=2

Solution

1. Isolate the term containing the exponential by subtracting 7 from both sides of the equation.

−3*e(−x)=2−7

−3*e(−x)=−5

2. Divide both sides by −3 to isolate the exponential function e(−x)

e(−x)=(−5)/(−3)

e(−x)=5/3

3. Apply the natural logarithm ln() to both sides to undo the exponential function.

ln(e(−x))=ln(5/3)

−x=ln(5/3)

4. Solve for x by multiplying both sides by −1

x=−ln(5/3)

5. Simplify the expression using the logarithmic property −ln(a)=ln(a(−1))

x=ln(3/5)

Final Answer

x=ln(3/5)

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