What is the inverse of ln((2x-1)/(3x+1))+2 ?

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

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inverse of ln((2x-1)/(3x+1))+2

inverse

ln (\frac{2 x - 1}{3 x + 1}) + 2

\frac{e ^{x - 2} + 1}{2 - 3 e ^{- 2 + x}}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{e ^{x - 2} + 1}{2 - 3 e ^{- 2 + x}}

f (x) = \frac{1}{5} (x + 7)

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

f (x) = 3 x + 12

f (x) = x^{2} - 6 x + 12

f (x) = x^{2} - 6 x + 17

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