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Find domain of f(x) = log5(log4(log3(log...

Find domain of `f(x) = log_5(log_4(log_3(log_2 x))) `

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`f(x) = log_(5)(log_(4)(log_(3)(log_(2)x)))`
We know that log(x) is defined when `x gt 0`
`:.` f(x) is defined only when
`log_(4)(log_(3)(log_(2)x)) gt 0` and `log_(3)(log_(2)x)) gt 0` and `log_(2)(x) gt 0, x gt 0`
`log_(3)(log_(3)(x)) gt 1` and `log_(2)(x) gt 1` and `x gt 1, x gt 0`
`log_(2)(x) gt 3` and `x gt 2`
`x gt 8`
`:.` f(x) is well defined when `x gt 8`.
`:. D_(f) = (8, oo)`
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