What is the inverse of f(x)=5+2^{x+1} ?

The inverse of f(x)=5+2^{x+1} is (ln(x-5))/(ln(2))-1

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inverse of f(x)=5+2^{x+1}

inverse

f (x) = 5 + 2^{x + 1}

\frac{ln ( x - 5 )}{ln ( 2 )} - 1

Solution steps

y = 5 + 2^{x + 1}

Replace

x

with

y

x = 5 + 2^{y + 1}

Solve for

y, x = 5 + 2^{y + 1}

\frac{ln ( x - 5 )}{ln ( 2 )} - 1

f (x) = 2 (x + 5)

\frac{3 x}{8 x ^{2} - 9}

\frac{x}{3}

f (x) = \frac{5}{13} x - 25

\frac{4}{1 - x}

What is the inverse of f(x)=5+2^{x+1} ?
The inverse of f(x)=5+2^{x+1} is (ln(x-5))/(ln(2))-1