Solve for x 10/(1+e^(-x))=2

Problem

10/(1+e(−x))=2

Solution

1. Multiply both sides by the denominator 1+e(−x) to clear the fraction.

10=2*(1+e(−x))

2. Divide both sides by 2 to isolate the term containing the exponential.

5=1+e(−x)

3. Subtract 1 from both sides to isolate the exponential expression.

4=e(−x)

4. Apply the natural logarithm ln() to both sides to solve for the exponent.

ln(4)=ln(e(−x))

5. Simplify the right side using the property ln(ea)=a

ln(4)=−x

6. Multiply by −1 to solve for x

x=−ln(4)

7. Rewrite the answer using the power property of logarithms ln(ab)=b*ln(a) if desired, noting 4=2

x=−2*ln(2)

Final Answer

10/(1+e(−x))=2⇒x=−ln(4)

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