$8.837=14 e^{-0.21 x}$
Simplify the final answer to get \(x = \boxed{2.191}\).
Step 1 :Given the equation \(8.837=14 e^{-0.21 x}\).
Step 2 :Isolate the exponential function on one side of the equation.
Step 3 :Take the natural logarithm of both sides of the equation to get rid of the exponential function.
Step 4 :This allows us to solve for x, where a = 8.837, b = 14, c = -0.21.
Step 5 :Calculate x to get x = 2.190999414663768.
Step 6 :Simplify the final answer to get \(x = \boxed{2.191}\).