What is the inverse of f(x)=3*5^{x-8}+17 ?

The inverse of f(x)=3*5^{x-8}+17 is (ln((x-17)/3))/(ln(5))+8

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inverse of f(x)=3*5^{x-8}+17

inverse

f (x) = 3 \cdot 5^{x - 8} + 17

\frac{ln ( \frac{x - 17}{3} )}{ln ( 5 )} + 8

Solution steps

y = 3 \cdot 5^{x - 8} + 17

Replace

x

with

y

x = 3 \cdot 5^{y - 8} + 17

Solve for

y, x = 3 \cdot 5^{y - 8} + 17

\frac{ln ( \frac{x - 17}{3} )}{ln ( 5 )} + 8

What is the inverse of f(x)=3*5^{x-8}+17 ?
The inverse of f(x)=3*5^{x-8}+17 is (ln((x-17)/3))/(ln(5))+8