What is the inverse of f(x)=(1/2)^{x-3} ?

The inverse of f(x)=(1/2)^{x-3} is -(ln(x))/(ln(2))+3

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inverse of f(x)=(1/2)^{x-3}

inverse

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

- \frac{ln ( x )}{ln ( 2 )} + 3

Solution steps

y = (\frac{1}{2})^{x - 3}

Replace

x

with

y

x = (\frac{1}{2})^{y - 3}

Solve for

y, x = (\frac{1}{2})^{y - 3}

- \frac{ln ( x )}{ln ( 2 )} + 3

f (7) = 5 - 3 x

f (x) = 23 - x^{2}

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

f (x) = (8 - x) (x + 2)

- \frac{3 x}{x ^{2} - 4}

What is the inverse of f(x)=(1/2)^{x-3} ?
The inverse of f(x)=(1/2)^{x-3} is -(ln(x))/(ln(2))+3