What is the inverse of (2+3*ln(x))/(4-ln(x)) ?

The inverse of (2+3*ln(x))/(4-ln(x)) is e^{-(2-4x)/(3+x)}

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inverse of (2+3*ln(x))/(4-ln(x))

inverse

\frac{2 + 3 \cdot ln ( x )}{4 - ln ( x )}

e^{- \frac{2 - 4 x}{3 + x}}

Solution steps

y = \frac{2 + 3 ln ( x )}{4 - ln ( x )}

Replace

x

with

y

x = \frac{2 + 3 ln ( y )}{4 - ln ( y )}

Solve for

y, x = \frac{2 + 3 \cdot ln ( y )}{4 - ln ( y )}

e^{- \frac{2 - 4 x}{3 + x}}

What is the inverse of (2+3*ln(x))/(4-ln(x)) ?
The inverse of (2+3*ln(x))/(4-ln(x)) is e^{-(2-4x)/(3+x)}