What is the inverse of f(x)=2(3^{x+1}) ?

The inverse of f(x)=2(3^{x+1}) is (ln(x/2))/(ln(3))-1

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inverse of f(x)=2(3^{x+1})

inverse

f (x) = 2 (3^{x + 1})

\frac{ln ( \frac{x}{2} )}{ln ( 3 )} - 1

Solution steps

y = 2 \cdot 3^{x + 1}

Replace

x

with

y

x = 2 \cdot 3^{y + 1}

Solve for

y, x = 2 3^{y + 1}

\frac{ln ( \frac{x}{2} )}{ln ( 3 )} - 1

\frac{3}{2 x - 1}

g (x) = 2^{- x}

\frac{x}{x - 9}

f (x) = \frac{7 x - 17}{12}

2^{x - 2} - 1

What is the inverse of f(x)=2(3^{x+1}) ?
The inverse of f(x)=2(3^{x+1}) is (ln(x/2))/(ln(3))-1