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^{4} - 16 x^{2}

f (x) = \frac{- 3 x + 2}{9 x - 8}

f (x) = x^{2} + 2 x - 5

8 x + 6 y = 18

f (x) = \frac{1}{4 + e ^{x}}

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)}