Step 1 :The given equation is \(e^{-0.171} = 0.93\).
Step 2 :To solve for \(L\), we need to isolate \(L\) on one side of the equation. We can do this by taking the natural logarithm (ln) of both sides of the equation.
Step 3 :The natural logarithm of \(e^{-0.171}\) is \(-0.171\), and we can use a calculator to find the natural logarithm of 0.93.
Step 4 :Now we have the natural logarithm of 0.93, which is -0.07257069283483537. This is the value of \(L\).
Step 5 :Final Answer: The solution is \(L = \boxed{-0.07257069283483537}\).