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

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

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

inverse

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

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

Solution steps

y = 5^{x - 2} + 3

Replace

x

with

y

x = 5^{y - 2} + 3

Solve for

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

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

f (x) = \frac{1 + e ^{- x}}{1 - e ^{- x}}

f (x) = \frac{x ^{3} - 27}{x - 3}

f (x) = x + 6 + 3

f (x) = ln (\frac{x}{18})

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

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