Solve the exponential equation.
\[
e^{-c}=2^{5 c}
\]
Final Answer: The solution to the equation is \(\boxed{0}\).
Step 1 :Given the exponential equation \(e^{-c}=2^{5 c}\).
Step 2 :Take the natural logarithm (ln) on both sides of the equation to bring down the exponents.
Step 3 :Solving for the variable c, we find that c = 0.
Step 4 :This means that when c is 0, both sides of the equation are equal.
Step 5 :Final Answer: The solution to the equation is \(\boxed{0}\).