What is the inverse of 1/2 log_{2x}(x) ?

The inverse of 1/2 log_{2x}(x) is e^{(2xln(2))/(1-2x)}

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inverse of 1/2 log_{2x}(x)

inverse

\frac{1}{2} lo g_{2 x} (x)

e^{\frac{2 x l n ( 2 )}{1 - 2 x}}

Solution steps

y = \frac{1}{2} lo g_{2 x} (x)

Replace

x

with

y

x = \frac{1}{2} lo g_{2 y} (y)

Solve for

y, x = \frac{1}{2} lo g_{2 y} (y)

e^{\frac{2 x l n ( 2 )}{1 - 2 x}}

What is the inverse of 1/2 log_{2x}(x) ?
The inverse of 1/2 log_{2x}(x) is e^{(2xln(2))/(1-2x)}