Step 1 :Given the exponential equation \(e^{1-4 x}=18\)
Step 2 :Take the natural logarithm on both sides of the equation to get \(1 - 4x = \ln(18)\)
Step 3 :Solve the equation for x to get \(x = \frac{1 - \ln(18)}{4}\)
Step 4 :Calculate the value of x to get \(x = -0.47259293947404113\)
Step 5 :Final Answer: The solution of the exponential equation \(e^{1-4 x}=18\) is \(\boxed{-0.47259293947404113}\)