If \( e^{5 x}=16 \), then \( x=\square \) Next Question \( \rightarrow \)

To solve for \( x \) in the equation \( e^{5x} = 16 \), take the natural logarithm of both sides: \[ 5x = \ln(16) \] Now, simply divide both sides by 5: \[ x = \frac{\ln(16)}{5} \] That's your solution for \( x \)! In a historical twist, the natural logarithm, denoted by \( \ln \), was popularized by mathematician Leonhard Euler in the 18th century. Euler discovered this function's remarkable properties that simplified complex calculations, paving the way for modern calculus. For a real-world application, natural logarithms are not just for math class—they’re used in fields like finance for compound interest calculations, in population models to predict growth, and even in analyzing data trends. Understanding how to manipulate such equations can help you make informed decisions in various life scenarios!