Find domain of the function `10^x+10^y=10`

Explanation

`10^y=10-10^x`

`10^y=10(1-10^(x-1))`

`log_10 10^y=log10(1-10^(x-1))`

`y=log_10 10+log_10(1-10^(x-1))`

`y=1+log_10(1-10^(x-1))`

`log_10(1-10^(n-1))`

`1-10^(x-1)>0`

`1>10^(x-1)`

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