SOLUTION: Find the inverse of f(x)=2^x. Here is where I went with this. Change f(x) to y so it would read y=2^x. Interchange the y and x to get x=2^y. I don't know how to write this on h

Algebra ->  Functions -> SOLUTION: Find the inverse of f(x)=2^x. Here is where I went with this. Change f(x) to y so it would read y=2^x. Interchange the y and x to get x=2^y. I don't know how to write this on h      Log On


   

Question 668382: Find the inverse of f(x)=2^x. Here is where I went with this. Change f(x) to y so it would read y=2^x. Interchange the y and x to get x=2^y. I don't know how to write this on here, but you would take the y square root of x and the y square root of 2^y to get y square root of x=2. This is where I get stuck. Thanks!
Found 3 solutions by Alan3354, lynnlo, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse of f(x)=2^x. Here is where I went with this. Change f(x) to y so it would read y=2^x. Interchange the y and x to get x=2^y.
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x=2^y
ln(x) = y*ln(2)
y = ln(x)/ln(2)
Or y+=+log%282%2Cx%29

Answer by lynnlo(4176) About Me  (Show Source):
You can put this solution on YOUR website!
f^-^1(x)=log(x)/log (2)

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse of f(x)=2^x. Here is where I went with this. Change f(x) to y so it would read y=2^x. Interchange the y and x to get x=2^y. 
You did fine that far.

Now with x = 2y we use the rule of equivalence of logarithms:

The exponential equation A = BC is equivalent to the logarithm equation C = logBA.

Use that to change the exponential equation x = 2y to: 

y = log2x

Then change y to f-1(x):

f-1(x) = log2x

Edwin