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

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

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

inverse

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

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

Solution steps

y = 3^{x + 2} + 1

Replace

x

with

y

x = 3^{y + 2} + 1

Solve for

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

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

ln (2 x) - 3

f (x) = ln (\frac{x}{19})

f (x) = 3 x - 17

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

2 x - 4

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