What is the inverse of ln((x-5)/(x-3)) ?

The inverse of ln((x-5)/(x-3)) is (-5+3e^x)/(e^x-1)

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inverse of ln((x-5)/(x-3))

inverse

ln (\frac{x - 5}{x - 3})

\frac{- 5 + 3 e ^{x}}{e ^{x} - 1}

Solution steps

y = ln (\frac{x - 5}{x - 3})

Replace

x

with

y

x = ln (\frac{y - 5}{y - 3})

Solve for

y, x = ln (\frac{y - 5}{y - 3})

\frac{- 5 + 3 e ^{x}}{e ^{x} - 1}

f (x) = \frac{x - 3}{x + 1}

tan (1)

f (x) = \frac{3 - 8 x}{4 + 7 x}

f (x) = 3 ln (\frac{x + 5}{2})

f (x) = - \frac{5}{4} x - 2

What is the inverse of ln((x-5)/(x-3)) ?
The inverse of ln((x-5)/(x-3)) is (-5+3e^x)/(e^x-1)