Solve for x 50/(1+e^(-x))=4

Problem

50/(1+e(−x))=4

Solution

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

50=4*(1+e(−x))

2. Divide both sides by 4 to isolate the term containing the exponential.

50/4=1+e(−x)

3. Simplify the fraction on the left side.

12.5=1+e(−x)

4. Subtract 1 from both sides to isolate e(−x)

11.5=e(−x)

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

ln(11.5)=ln(e(−x))

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

ln(11.5)=−x

7. Multiply by −1 to solve for x

x=−ln(11.5)

Final Answer

50/(1+e(−x))=4⇒x=−ln(11.5)

Want more problems? Check here!