What is the inverse of f(x)=5^{x-2}+8 ?

The inverse of f(x)=5^{x-2}+8 is (ln(x-8))/(ln(5))+2

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inverse of f(x)=5^{x-2}+8

inverse

f (x) = 5^{x - 2} + 8

\frac{ln ( x - 8 )}{ln ( 5 )} + 2

Solution steps

y = 5^{x - 2} + 8

Replace

x

with

y

x = 5^{y - 2} + 8

Solve for

y, x = 5^{y - 2} + 8

\frac{ln ( x - 8 )}{ln ( 5 )} + 2

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

2 x^{2} - 6

4 x - 2 y = - 4

f (x) = ln (5 - 4 x^{2})

f (x) = \frac{x ^{2} - x + 6}{4 x - 1}

What is the inverse of f(x)=5^{x-2}+8 ?
The inverse of f(x)=5^{x-2}+8 is (ln(x-8))/(ln(5))+2