Find the domain of definition of the function f(x) = `log_10 log_10 log_10 { (x + 1)(x - 2)}`.

Explanation

f(x)=`log_10 log_10 log_10 {(x + 1)(x - 2)}`
Let , z = (x + 1) ( x- 2)
Now, `log_10 log_10(z) lt 0`i.e, `log_10 z gt 10`
`rArr (x + 1)(x -2) gt 10 rArr x62 - x - 12 gt 0`
` rArr x in (- infty, -3) cup (4 , infty)`
`therefore` Domain of definition of f(x) is `(- infty , -3) cup ( 4 , infty)`