What is the inverse of f(x)=5(0.5)^{-x} ?

The inverse of f(x)=5(0.5)^{-x} is -(ln(x/5))/(ln(0.5))

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inverse of f(x)=5(0.5)^{-x}

inverse

f (x) = 5 (0.5)^{- x}

- \frac{ln ( \frac{x}{5} )}{ln ( 0.5 )}

Solution steps

y = 5 \cdot 0. 5^{- x}

Replace

x

with

y

x = 5 \cdot 0. 5^{- y}

Solve for

y, x = 50. 5^{- y}

- \frac{ln ( \frac{x}{5} )}{ln ( 0.5 )}

What is the inverse of f(x)=5(0.5)^{-x} ?
The inverse of f(x)=5(0.5)^{-x} is -(ln(x/5))/(ln(0.5))