# How do you find the inverse of # f(x) = 3log(x-1)#?

Manipulate to give:

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To find the inverse of the function (f(x) = 3\log(x - 1)), we switch the roles of (x) and (y) and solve for (y).

- Start with the original function: (f(x) = 3\log(x - 1)).
- Replace (f(x)) with (y): (y = 3\log(x - 1)).
- Swap (x) and (y): (x = 3\log(y - 1)).
- Solve for (y): [x = 3\log(y - 1)] [x/3 = \log(y - 1)] [10^{x/3} = y - 1] [y = 10^{x/3} + 1]

So, the inverse function is (f^{-1}(x) = 10^{x/3} + 1).

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