What is the inverse of f(x)=54.577*e^{-x*4.493} ?

The inverse of f(x)=54.577*e^{-x*4.493} is -(ln(\frac{1000x)/(54577))}{4.493}

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inverse of f(x)=54.577e^{-x4.493}

inverse

f (x) = 54.577 \cdot e^{- x \cdot 4.493}

- \frac{ln ( \frac{1000 x}{54577} )}{4.493}

Solution steps

y = 54.577 e^{- x \cdot 4.493}

Replace

x

with

y

x = 54.577 e^{- y \cdot 4.493}

Solve for

y, x = 54.577 \cdot e^{- y \cdot 4.493}

- \frac{ln ( \frac{1000 x}{54577} )}{4.493}

What is the inverse of f(x)=54.577*e^{-x*4.493} ?
The inverse of f(x)=54.577*e^{-x*4.493} is -(ln(\frac{1000x)/(54577))}{4.493}