What is the inverse of (3e^x+1)/(9e^x-1) ?

The inverse of (3e^x+1)/(9e^x-1) is ln((1+x)/(3(-1+3x)))

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inverse of (3e^x+1)/(9e^x-1)

inverse

\frac{3 e ^{x} + 1}{9 e ^{x} - 1}

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

Solution steps

y = \frac{3 e ^{x} + 1}{9 e ^{x} - 1}

Replace

x

with

y

x = \frac{3 e ^{y} + 1}{9 e ^{y} - 1}

Solve for

y, x = \frac{3 e ^{y} + 1}{9 e ^{y} - 1}

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

What is the inverse of (3e^x+1)/(9e^x-1) ?
The inverse of (3e^x+1)/(9e^x-1) is ln((1+x)/(3(-1+3x)))