SOLUTION: Find the inverse function of f. f(x) = log3(x - 2) (The three represents log base 3 of (x-2) )

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Question 869711: Find the inverse function of f.
f(x) = log3(x - 2)
(The three represents log base 3 of (x-2) )
Found 2 solutions by josgarithmetic, jim_thompson5910:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=log%283%2C%28x-2%29%29.

f(x) is an exponent, same as logarithm. You know the base...
g(x) assigned as inverse.
f%28g%28x%29%29=highlight_green%28log%283%2C%28g%28x%29-2%29%29=x%29.
Change into exponential form.
3%5Ex=g%28x%29-2
highlight%28g%28x%29=3%5Ex%2B2%29.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Replace f(x) with y. Swap x and y. Then solve for y.


f%28x%29+=+log%283%2C%28x-2%29%29


y+=+log%283%2C%28x-2%29%29


x+=+log%283%2C%28y-2%29%29


3%5Ex+=+y-2


3%5Ex%2B2+=+y


y=3%5Ex%2B2


The inverse function is f%5E%28-1%29%28x%29+=+3%5Ex%2B2