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

Problem

e(−2*x)=7

Solution

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

ln(e(−2*x))=ln(7)

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

−2*x=ln(7)

3. Divide both sides by −2 to solve for x

x=ln(7)/(−2)

4. Rewrite the expression to place the negative sign in front of the fraction.

x=−ln(7)/2

Final Answer

e(−2*x)=7⇒x=−ln(7)/2

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