Solving for three constant values using three columns of data

So I have three columns of data (A, B, and C) and I want to find three constant values (x, y, and z) that I can plug into an equation like:

C = x * [A^y * constant^z + B^y* other_constant ^z]

How can excel solve for average values of x, y, and z and possibly output information on the error in those values?

I would probably treat it like a non-linear regression problem.

Spreadsheet would look something like:

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Then call the Solver tool and tell it to 1) Set the sum(E4:E40) cell 2) to a minimum 3) by changing x,y,z