Find domain of the function log10 log10...

Find domain of the function ` log_10 log_10 log_10 log_10 log_10 x`

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`log_10log_10log_10log_10 x>0`
`log_10log_10log_10 x>10^0`
`log_10^xlog_10^x>10^1`
`log_10^xlog_10^x>10`
`log_10^x>10^10`
`x>10^(10^10)`.

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