SOLUTION: How do you find the inverse of the function: f(x)=5^x

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Question 27431: How do you find the inverse of the function: f(x)=5^x
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
To find the inverse function, we basically need to re-order the function f(x)=5%5Ex.

Let y+=+5%5Ex. We need to find what x equals in terms of "y". This is the inverse function.

So, y+=+5%5Ex --> take logs. Best base is to base5, which i shall just write as "log".

--> log(y) = log%285%5Ex%29
--> log(y) = x

- the log and the 5 "cancel" each other...that is why i chose log to base5.

so, the inverse function f%5E%28-1%29%28y%29+=+log%28y%29 ... remember, this is log to base5.

However, we tend to write equations in terms of x rather than y, so we just quote x rather than y..no great magic involved...

--> f%5E%28-1%29%28x%29+=+log%28x%29

jon.