What is the inverse of f(x)=3^{2x-4}+5 ?

The inverse of f(x)=3^{2x-4}+5 is (ln(81(x-5)))/(2ln(3))

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inverse of f(x)=3^{2x-4}+5

inverse

f (x) = 3^{2 x - 4} + 5

\frac{ln ( 81 ( x - 5 ) )}{2 ln ( 3 )}

Solution steps

y = 3^{2 x - 4} + 5

Replace

x

with

y

x = 3^{2 y - 4} + 5

Solve for

y, x = 3^{2 y - 4} + 5

\frac{ln ( 81 ( x - 5 ) )}{2 ln ( 3 )}

f (x) = \frac{2 - 5 x}{3 x + 4}

f (x) = \frac{2}{( x - 1 ) ^{2}} - \frac{20}{9}

2 (x + 3)^{2} - 5

f (x) = \frac{9 x}{x ^{2} - 1}

f (x) = x^{2} + 8 x - 9

What is the inverse of f(x)=3^{2x-4}+5 ?
The inverse of f(x)=3^{2x-4}+5 is (ln(81(x-5)))/(2ln(3))