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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

y = 4 x + 4

3 (x + 4)^{2} - 2

g (x) = \frac{2}{4 - x}

sin (2 θ)

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