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\( e ^ { - 0.5 } = e ^ { n } \quad n = ? \)

Ask by Dawson Mcguire. in India
Jan 21,2025

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\( n = -0.5 \)

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The Deep Dive

To solve for \( n \) in the equation \( e^{-0.5} = e^n \), we can take the natural logarithm of both sides. Since the natural logarithm and the exponential function are inverses, we have: \[ \ln(e^{-0.5}) = \ln(e^n) \] This simplifies to: \[ -0.5 = n \] So, \( n = -0.5 \). Well done, you just tackled an exponential equation! Remember, the key to working with exponents and logarithms is to leverage their properties, particularly that they are inverses of each other. Keep practicing, and you'll become a pro at these kinds of problems!

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