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

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

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inverse of f(x)=log_{3}(4^x-4)

inverse

f (x) = lo g_{3} (4^{x} - 4)

\frac{ln ( 3 ^{x} + 4 )}{2 ln ( 2 )}

Solution steps

y = lo g_{3} (4^{x} - 4)

Replace

x

with

y

x = lo g_{3} (4^{y} - 4)

Solve for

y, x = lo g_{3} (4^{y} - 4)

\frac{ln ( 3 ^{x} + 4 )}{2 ln ( 2 )}

3 x^{4} - 28 x^{3} + 60 x^{2}

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

\frac{- 3}{x - 1}

f (x) = \frac{4}{n} - 3

f (x) = \frac{1 - 4 t}{2 + t}

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