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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

y = - x^{2} + 9

(x - 2)^{2} + 4

x^{3} + 6 x^{2} - 63 x

(- 15, 11), (- 22, - 10)

1.5 sin (4 x)

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