What is the inverse of f(x)=2^{2^x} ?

The inverse of f(x)=2^{2^x} is (ln(\frac{ln(x))/(ln(2)))}{ln(2)}

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inverse of f(x)=2^{2^x}

inverse

f (x) = 2^{2^{x}}

\frac{ln ( \frac{l n ( x )}{l n ( 2 )} )}{ln ( 2 )}

Solution steps

y = 2^{2^{x}}

Replace

x

with

y

x = 2^{2^{y}}

Solve for

y, x = 2^{2^{y}}

\frac{ln ( \frac{l n ( x )}{l n ( 2 )} )}{ln ( 2 )}

What is the inverse of f(x)=2^{2^x} ?
The inverse of f(x)=2^{2^x} is (ln(\frac{ln(x))/(ln(2)))}{ln(2)}