What is the inverse of f(x)=-2/3 log_{10}(x-1)+2 ?

The inverse of f(x)=-2/3 log_{10}(x-1)+2 is 10^{-(3x-6)/2}+1

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inverse of f(x)=-2/3 log_{10}(x-1)+2

inverse

1 0^{- \frac{3 x - 6}{2}} + 1

Solution steps

y = - \frac{2}{3} lo g_{10} (x - 1) + 2

Replace

x

with

y

x = - \frac{2}{3} lo g_{10} (y - 1) + 2

Solve for

y, x = - \frac{2}{3} lo g_{10} (y - 1) + 2

1 0^{- \frac{3 x - 6}{2}} + 1

What is the inverse of f(x)=-2/3 log_{10}(x-1)+2 ?
The inverse of f(x)=-2/3 log_{10}(x-1)+2 is 10^{-(3x-6)/2}+1