What is the inverse of f(x)=2^{-3x+4} ?

The inverse of f(x)=2^{-3x+4} is -(ln(x)-4ln(2))/(3ln(2))

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inverse of f(x)=2^{-3x+4}

inverse

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

- \frac{ln ( x ) - 4 ln ( 2 )}{3 ln ( 2 )}

Solution steps

y = 2^{- 3 x + 4}

Replace

x

with

y

x = 2^{- 3 y + 4}

Solve for

y, x = 2^{- 3 y + 4}

- \frac{ln ( x ) - 4 ln ( 2 )}{3 ln ( 2 )}

What is the inverse of f(x)=2^{-3x+4} ?
The inverse of f(x)=2^{-3x+4} is -(ln(x)-4ln(2))/(3ln(2))