SOLUTION: What is the inverse function of: f(x) = (1/2)^x

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Question 1116083: What is the inverse function of:
f(x) = (1/2)^x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
What is the inverse function of:
f%28x%29+=+%281%2F2%29%5Ex
y = f(x)
y+=+%281%2F2%29%5Ex
Swap x and y, solve for y
x+=+%281%2F2%29%5Ey
Find the y root of both sides
x%5E%281%2Fy%29+=+1%2F2
Using common logs
log%28%28x%5E%281%2Fy%29%29%29+=+log%28%281%2F2%29%29
the log equiv of exponents
%281%2Fy%29log%28%28x%29%29+=+log%28%281%2F2%29%29
multiply both sides by y
log%28%28x%29%29+=+y%2Alog%28%281%2F2%29%29
divide both sides by log(1/2)
log%28%28x%29%29%2Flog%28%281%2F2%29%29 = y
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