Solve for x e^(4x)=5.7

Problem

e(4*x)=5.7

Solution

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

ln(e(4*x))=ln(5.7)

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

4*x=ln(5.7)

3. Isolate the variable x by dividing both sides of the equation by 4

x=ln(5.7)/4

4. Calculate the numerical value using the approximate value of ln(5.7)≈1.740466

x≈0.435116

Final Answer

x=ln(5.7)/4

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