solve(Eq(1/(10**(-x) + 10**(-y)), 10**z), z)
Out[10]: 
⎡        ⎛  x        y⎞          ⎛  x + y⎞            ⎤
⎢- log⎝10  + 10 ⎠ + log⎝10     ⎠              ⎥
⎢───────────────────────────────⎥
⎣            log(10)                                      ⎦

That's not much of an answer.  Should be:

z = -log10(10**-x + 10**-y)

What am I doing wrong?

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