What is the inverse of (ln(x)+3)/(1-2ln(x)) ?

The inverse of (ln(x)+3)/(1-2ln(x)) is e^{-(3-x)/(1+2x)}

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inverse of (ln(x)+3)/(1-2ln(x))

inverse

\frac{ln ( x ) + 3}{1 - 2 ln ( x )}

e^{- \frac{3 - x}{1 + 2 x}}

Solution steps

y = \frac{ln ( x ) + 3}{1 - 2 ln ( x )}

Replace

x

with

y

x = \frac{ln ( y ) + 3}{1 - 2 ln ( y )}

Solve for

y, x = \frac{ln ( y ) + 3}{1 - 2 ln ( y )}

e^{- \frac{3 - x}{1 + 2 x}}

y = 2 x (4 - x)

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

f (x) = e^{2 x} + 4 e^{x} - 5

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

f (y) = x^{2}

What is the inverse of (ln(x)+3)/(1-2ln(x)) ?
The inverse of (ln(x)+3)/(1-2ln(x)) is e^{-(3-x)/(1+2x)}