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The domain of f(x) = log(a1)log(a2)log(...

The domain of ` f(x) = log_(a1)log_(a2)log_(a3)log_(a4)(x)` `(a_i>0)` is

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`f(x) = log_(a_1)log_(a_2)log_(a_3)log_(a_4)(x)`
For `f(x)` to be defined ,
(i)`x gt 0`.
(ii)`log_(a_4)(x) gt 0 => x gt (a_4)^0 => x gt 1`
(iii)`log_(a_3)log_(a_4)(x) gt 0 => log_(a_4)x gt (a_3)^0 `
`=>x gt (a_4)^1 => x gt a_4`
(iv)`log_(a_2)log_(a_3)log_(a_4)(x) gt 0`
`=> log_(a_3)log_(a_4)(x) gt (a_2)^0`
...
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