if $e^{5 x}=27$, then $x=$

Step 1 ：The given equation is \(e^{5x} = 27\).

Step 2 ：Take the natural logarithm (ln) of both sides of the equation to get \(5x = \ln(27)\).

Step 3 ：Divide both sides of the equation by 5 to solve for x, \(x = \frac{\ln(27)}{5}\).

Step 4 ：Calculate the value of x to get \(x = 0.6591673732008658\).

Step 5 ：Final Answer: \(x = \boxed{0.6591673732008658}\)