SOLUTION: find the inverse of the function y=log5(x^2) the five is small

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Question 277539: find the inverse of the function
y=log5(x^2)
the five is small
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
y=log%285%2C+%28x%5E2%29%29
To find an inverse:
  1. Swap the x's and y's. Wherever you see an x, write y and wherever you see y, write x. This creates the inverse equation.
  2. If possible solve the new equation for y

Let's see how this works on your equation.
1. Swap the x's and y's:
x=log%285%2C+%28y%5E2%29%29
2. Solve for y, if possible.
To solve our equation for y we start by rewriting the equation in exponential form. (This gets y out the of the argument of the logarithm.)
5%5Ex+=+y%5E2
At this point we get stuck. We cannot solve this for y. (At least not for a single-valued expression for y.) So the inverse of your original function is not a function. The inverse can be expressed with any of the following:
x=log%285%2C+%28y%5E2%29%29
5%5Ex+=+y%5E2
(sqrt%285%5Ex%29+=+y or -sqrt%285%5Ex%29+=+y)