Problem

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

Answer

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Answer

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

Steps

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: \(x = \boxed{0.6591673732008658}\)

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