What is the inverse of f(x)=3(1/4)^{x-2}+4 ?

The inverse of f(x)=3(1/4)^{x-2}+4 is -(ln((x-4)/3))/(2ln(2))+2

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inverse of f(x)=3(1/4)^{x-2}+4

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

What is the inverse of f(x)=3(1/4)^{x-2}+4 ?
The inverse of f(x)=3(1/4)^{x-2}+4 is -(ln((x-4)/3))/(2ln(2))+2