What is the inverse of f(x)=4^{2x+1} ?

The inverse of f(x)=4^{2x+1} is (ln(x)-2ln(2))/(4ln(2))

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inverse of f(x)=4^{2x+1}

inverse

f (x) = 4^{2 x + 1}

\frac{ln ( x ) - 2 ln ( 2 )}{4 ln ( 2 )}

Solution steps

y = 4^{2 x + 1}

Replace

x

with

y

x = 4^{2 y + 1}

Solve for

y, x = 4^{2 y + 1}

\frac{ln ( x ) - 2 ln ( 2 )}{4 ln ( 2 )}

f (x) = 2 x - 1 - 8

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

f (x) = ln (\frac{x + 1}{x - 1})

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

f (x) = 9 + 10 x

What is the inverse of f(x)=4^{2x+1} ?
The inverse of f(x)=4^{2x+1} is (ln(x)-2ln(2))/(4ln(2))