Solve for x 1025/(8+e^(4x))=5

Problem

1025/(8+e(4*x))=5

Solution

1. Multiply both sides by the denominator 8+e(4*x) to clear the fraction.

1025=5*(8+e(4*x))

2. Divide both sides by 5 to isolate the term containing the exponential.

1025/5=8+e(4*x)

205=8+e(4*x)

3. Subtract 8 from both sides to isolate the exponential term e(4*x)

205−8=e(4*x)

197=e(4*x)

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

ln(197)=ln(e(4*x))

ln(197)=4*x

5. Divide by 4 to solve for x

x=ln(197)/4

Final Answer

1025/(8+e(4*x))=5⇒x=ln(197)/4

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