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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

x^{3} - 5 x

(- 5.4) (0.6)

f (x) = - \frac{1}{2} x^{2} + 4 x + 3

f (x) = - 5 x

(35), (32)

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