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

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

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

inverse

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

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

Solution steps

y = ln (x) - ln (x - 1)

Replace

x

with

y

x = ln (y) - ln (y - 1)

Solve for

y, x = ln (y) - ln (y - 1)

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

2 x + 2

f (x) = \frac{x ^{3}}{3} - 9 x

f (x) = x^{2} - 4 x

\frac{3 x + 6}{x ^{2} - x - 2}

f (x) = 4 x - 10

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