What is the inverse of f(x)=3^{2x+4}+3 ?

The inverse of f(x)=3^{2x+4}+3 is (ln(x-3)-4ln(3))/(2ln(3))

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inverse of f(x)=3^{2x+4}+3

inverse

f (x) = 3^{2 x + 4} + 3

\frac{ln ( x - 3 ) - 4 ln ( 3 )}{2 ln ( 3 )}

Solution steps

y = 3^{2 x + 4} + 3

Replace

x

with

y

x = 3^{2 y + 4} + 3

Solve for

y, x = 3^{2 y + 4} + 3

\frac{ln ( x - 3 ) - 4 ln ( 3 )}{2 ln ( 3 )}

What is the inverse of f(x)=3^{2x+4}+3 ?
The inverse of f(x)=3^{2x+4}+3 is (ln(x-3)-4ln(3))/(2ln(3))