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 )}

f (x) = \frac{x}{x - 8}

(x + 5)^{3}

f (x) = \frac{4 x - 9}{- 5 x}

f (x) = \frac{( 3 x - 5 )}{( 2 x - 7 )}

f (x) = 3 (\frac{1}{4})^{x - 2} + 4

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)}