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

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

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inverse of (2^x)/(1+2^x)

inverse

\frac{2 ^{x}}{1 + 2 ^{x}}

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

Solution steps

y = \frac{2 ^{x}}{1 + 2 ^{x}}

Replace

x

with

y

x = \frac{2 ^{y}}{1 + 2 ^{y}}

Solve for

y, x = \frac{2 ^{y}}{1 + 2 ^{y}}

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

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