SOLUTION: If f(x) = log3 (x + 1), what is f−1(2)?

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Question 934844: If f(x) = log3 (x + 1), what is f−1(2)?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+log%283%2C+%28x+%2B+1%29%29}, find inverse
since f%28x%29=y, we have
y+=+log%283%2C+%28x+%2B+1%29%29,...swap x and y
x=+log%283%2C+%28y+%2B+1%29%29...solve for y, change the base
x=+log%28+%28y+%2B+1%29%29%2Flog%283%29
x%2Alog%283%29=+log%28+%28y+%2B+1%29%29
log%283%5Ex%29=+log%28+%28y+%2B+1%29%29 ...if log same, then
3%5Ex=+y+%2B+1
3%5Ex-1=+y+
so, inverse is:
f%5E%28-1%29+%28x%29+=+3%5Ex-1
now find f%5E%28-1%29+%282%29+
f%5E%28-1%29+%282%29+=+3%5E2-1
f%5E%28-1%29+%282%29+=+9-1
f%5E%28-1%29+%282%29+=+8