What is the inverse of f(x)=20-20e^{-ln(10)*x} ?

The inverse of f(x)=20-20e^{-ln(10)*x} is -(ln(-\frac{x-20)/(20))}{ln(10)}

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inverse of f(x)=20-20e^{-ln(10)*x}

inverse

f (x) = 20 - 20 e^{- l n (10) \cdot x}

- \frac{ln ( - \frac{x - 20}{20} )}{ln ( 10 )}

Solution steps

y = 20 - 20 e^{- l n (10) x}

Replace

x

with

y

x = 20 - 20 e^{- l n (10) y}

Solve for

y, x = 20 - 20 e^{- l n (10) \cdot y}

- \frac{ln ( - \frac{x - 20}{20} )}{ln ( 10 )}

What is the inverse of f(x)=20-20e^{-ln(10)*x} ?
The inverse of f(x)=20-20e^{-ln(10)*x} is -(ln(-\frac{x-20)/(20))}{ln(10)}