Solve for x 400/(1+e^(-x))=350

Problem

400/(1+e(−x))=350

Solution

1. Isolate the denominator by multiplying both sides by 1+e(−x) and dividing by 350

400/350=1+e(−x)

2. Simplify the fraction on the left side.

8/7=1+e(−x)

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

8/7−1=e(−x)

1/7=e(−x)

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

ln(1/7)=ln(e(−x))

ln(1)−ln(7)=−x

5. Simplify using the property ln(1)=0

0−ln(7)=−x

−ln(7)=−x

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

x=ln(7)

Final Answer

400/(1+e(−x))=350⇒x=ln(7)

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