What is the inverse of log_{5}((1-x)/(1+x)) ?

The inverse of log_{5}((1-x)/(1+x)) is (1-5^x)/(5^x+1)

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inverse of log_{5}((1-x)/(1+x))

inverse

lo g_{5} (\frac{1 - x}{1 + x})

\frac{1 - 5 ^{x}}{5 ^{x} + 1}

Solution steps

y = lo g_{5} (\frac{1 - x}{1 + x})

Replace

x

with

y

x = lo g_{5} (\frac{1 - y}{1 + y})

Solve for

y, x = lo g_{5} (\frac{1 - y}{1 + y})

\frac{1 - 5 ^{x}}{5 ^{x} + 1}

What is the inverse of log_{5}((1-x)/(1+x)) ?
The inverse of log_{5}((1-x)/(1+x)) is (1-5^x)/(5^x+1)