What is the inverse of f(x)=2^{3^x} ?

The inverse of f(x)=2^{3^x} is (ln(\frac{ln(x))/(ln(2)))}{ln(3)}

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inverse of f(x)=2^{3^x}

inverse

f (x) = 2^{3^{x}}

\frac{ln ( \frac{l n ( x )}{l n ( 2 )} )}{ln ( 3 )}

Solution steps

y = 2^{3^{x}}

Replace

x

with

y

x = 2^{3^{y}}

Solve for

y, x = 2^{3^{y}}

\frac{ln ( \frac{l n ( x )}{l n ( 2 )} )}{ln ( 3 )}

f (x) = \frac{8}{9 + 4 x}

f (x) = \frac{1 + 3 x ^{3}}{2 - 5 x ^{3}}

y = 5^{x} + 7

f (x) = \frac{2}{3} x + \frac{4}{3}

y = \frac{x - 2}{x + 3}

What is the inverse of f(x)=2^{3^x} ?
The inverse of f(x)=2^{3^x} is (ln(\frac{ln(x))/(ln(2)))}{ln(3)}