Problem

Find the solution of the exponential equation $e^{1-4 x}=18$

Answer

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Answer

Final Answer: The solution of the exponential equation \(e^{1-4 x}=18\) is \(\boxed{-0.47259293947404113}\)

Steps

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 \(\boxed{-0.47259293947404113}\)

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