What is the inverse of f(x)=500(1/2)^{x/(272)} ?

The inverse of f(x)=500(1/2)^{x/(272)} is -(272ln(x/(500)))/(ln(2))

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inverse of f(x)=500(1/2)^{x/(272)}

inverse

f (x) = 500 (\frac{1}{2})^{\frac{x}{272}}

- \frac{272 ln ( \frac{x}{500} )}{ln ( 2 )}

Solution steps

y = 500 (\frac{1}{2})^{\frac{x}{272}}

Replace

x

with

y

x = 500 (\frac{1}{2})^{\frac{y}{272}}

Solve for

y, x = 500 (\frac{1}{2})^{\frac{y}{272}}

- \frac{272 ln ( \frac{x}{500} )}{ln ( 2 )}

f (x) = 0.5 + (\frac{5}{0.2 x})

2^{x - 2}

f (x) = - (x - 2)^{2} - 3

\frac{3}{4 x + 3}

What is the inverse of f(x)=500(1/2)^{x/(272)} ?
The inverse of f(x)=500(1/2)^{x/(272)} is -(272ln(x/(500)))/(ln(2))