What is the inverse of f(x)=(ln(x))/(1-ln(x)) ?

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

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inverse of f(x)=(ln(x))/(1-ln(x))

inverse

f (x) = \frac{ln ( x )}{1 - ln ( x )}

e^{\frac{x}{x + 1}}

Solution steps

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

Replace

x

with

y

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

Solve for

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

e^{\frac{x}{x + 1}}

f (x) = ln (x - 1) - ln (2 x + 1)

f (x) = lo g_{5} (2 x + 4)

f (x) = \frac{2 x - 7}{5 x + 1}

f (x) = 3 sin (x) + 2

7 + ln (3 x + 1)

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